Originally the states were considered as a critical part of the system of checks and balances in our federal form of republic. Let's take a look at the Federalist No. 28 by Alexander Hamilton.
It may safely be received as an axiom in our political system, that the State governments will, in all possible contingencies, afford complete security against invasions of the public liberty by the national authority. Projects of usurpation cannot be masked under pretenses so likely to escape the penetration of select bodies of men, as of the people at large. The legislatures will have better means of information. They can discover the danger at a distance; and possessing all the organs of civil power, and the confidence of the people, they can at once adopt a regular plan of opposition, in which they can combine all the resources of the community. They can readily communicate with each other in the different States, and unite their common forces for the protection of their common liberty.

Can the President enter into a treaty that does away with the Constitution?
Article VI, Clause 2 of the Constitution declares that "This Constitution, and the Laws of the United States which shall be made in Pursuance thereof; and all Treaties made, or which shall be made, under the Authority of the United States, shall be the supreme Law of the Land." At the time of the writing of the Constitution the Founders wanted to be sure that no state would have jurisdictional conflicts between the states and the federal government, at least limiting it. So they declared that the Constitution is the supreme law of the land. All federal laws that were in accordance with the Constitution were also superior to state laws.
The Founders also wanted to be sure that state laws would not conflict with the treaties that the nation entered into. Such conflicts or potential conflicts the Founders realized would greatly weaken the nation's ability to negotiate treaties. Just as Clause 2 does not imply that federal laws are superior to the Constitution it does not imply that treaties are superior. The Supreme Court declaed that a treaty cannot obligate the violation of Constitutional grarantees, such as those found in the Bill of Rights. (see Reid v. Covert 1957)
Furthermore, since a treaty is to be considered on the same level as any other federal law then Congress can repeal the treaty as they can repeal a law.
Under Supreme Court precedents, the last expression of the sovereign will controls, so an act of Congress that is in conflict with a treaty will control if the act became law after the Senate ratified the treaty, and vice versa. (Gary Lawson, The Heritage Guide to the Constitution  , pg. 294)

The Founders recognized that the Constitution that they offered the country was not perfect and would have to be altered from time to time. Just as with a contract between certain parties the Constitution had to include a means to "improve and perpetuate" the Constitution. It is found in Article V.
They provided two mean by which a change to the Constitution could be proposed. The Congress could by a two-thirds vote in each of the House and Senate propose a specific amendment. Or, two-thirds of the state legislatures could vote to convene a constitutional convention in which an amendment or amendments could be proposed, considered and voted on to forward to the states for ratification.
However the amendment(s) are presented, the ratification by three-forths of the states is required before the amendment can be added to the Constitution. The ratification by the states can be either by the state legislature or by state convention called for by the state legislature.
Although it is recognized that the Founders deliberately made the amending process difficult to achieve (so that the national charter would not be changed recklessly), nevertheless Washington warned that whenever there was a need for a modification, it should be done through the amending process and not by usurpation. In his Farewell Address he said "Let there be no change by usurpation." The improper delegation of authourity by the Congress and the usurpation of authority by the executive and judicial branches are said to be responsible for the most serious problems presently assailing the country.
(W.Cleon Skousen, The Making of America: The Substance and Meaning of the Constitution  , pg. 645
So herein is the only legal way that the Constitution can be changed, superseded or nullified.

The one principle that I believe wraps together all of the rest of the principles of a market economy is the concept of limited government. Adam Smith, author of The Wealth of Nations (Bantam Classics)  , wrote the following:
The statesman who should attempt to direct private people in what manner they ought to employ their capitals, would not only load himself with a most unnecessary attention, but assume an authority which could safely be trusted to no council and senate whatever, and which would nowhere be so dangerous as in the hands of a man who had folly and presumption enough to fancy himself fit to exercise it.
Governments are by nature unable to quickly respond to a ever changing market. Government is unable to avoid inserting bias into the decision process, giving favor to one sector or another of the market, thus directly or indirectly suppressing other sectors. One should read The Road to Serfdom, Fiftieth Anniversary Edition; by F. A. Hayek  in order to gain a fuller appreciation of the folly of government controlled economies.
(At the same time that government should be restrained from controlling the market there is a proper place for government and its courts in order to enforce contracts and to ensure a "level playing field," i.e. preventing monopolies and such.)
The two items in the Constitution that restricts the federal government most are Amendments IX and X, part of The Bill of Rights. They read:
Amendment IX: The enumeration in the Constitution, of certain rights, shall not be construed to deny or disparage others retained by the people.
Amendment X: The powers not delegated to the United States by the Constitution, nor prohibited by it to the States, are reserved to the States respectively, or to the people.

Constitutional Protection of Private Property
- by George Sweeney
 
The moment the idea is admitted into society that property is not as sacred as the law of God, and that there is not a force of law and public justice to protect it, anarchy and tyranny commence.
- John Adams
The Founding Fathers understood the vital importance of private property and its connection to liberty. Property is the resource from which we can clothe, shelter and feed ourselves and our families. A people denied the right to own property are under the control of those who control those resources. (see The Mystery of Capital: Why Capitalism Triumphs in the West and Fails Everywhere Else  by Hernando de Soto)
In order to sustain liberty there had to be the general right to private property and this was enacted into the Supreme Law of America, The Constitution. Let's look at what is in The Constitution that protects private property.
In Article I, Section 8- "To promote the Progress of Science and useful Arts, by securing for limited Times to Authors and Inventors the exclusive Right to their respective Writing and Discoveries;..." This protects inventions and intellectual property such as a novel.
Article I, Sections 9, and 10, the authority to pass Bills of Attainder or ex post facto Law was denied to the federal and state governments respectively. This respectively protected the rights of inheritance and allowed a property owner the chance to plan ahead knowing that the state could not retroactively declare his or her actions illegal.
Amendment IV protects from "unreasonable searches and seizures" of a person's person, house, papers, or effects.
Amendment V limits government from depriving a person of their property without due process of law, i.e. trial. Then Amendment XIV extended the right of due process to all of the states.

The Security and Prosperity Partnership of North America summit in Canada released a plan that established U.N. law along with regulations by the World Trade Organization and World Health Organization as supreme over U.S. law and set the stage for militarizing the management of continental health emergencies.
-Worldnetdaily.com, Tuesday, August 28, 2007 by Jerome R. Corsi
As the question above states, Is a presidential agreement the same as law? Looking at Article I, Section 10 we see reference to "treaty, alliance or confederation." This has lead many to believe that the Founding Fathers considered there to be different levels of agreements with foreign powers. However this clause starts with "No State." I am of the opinion that this limits the states from entering foreign agreements.
As for the Federal Government we need to look at Article II, Section 2, Clause 2 that states that the President "shall have Power, by and with the Advice and consent of the Senate, to make Treaties." This requires Senate approval of all Treaties. The debate has been on the levels of agreement that do not require Senate approval. Basically the pattern has been if the agreement is within the scope of law passed by congress than no further approval is needed. However anything outside the scope of existing law requires approval.  
In Article VI, Clause 2 Treaties are given the same weight as law passed by Congress and signed by the President. This is why I believe the Founding Fathers, though they did not comment much on the subject, determined that the Senate must approve all Treaties, seeing that they gave ALL legislative authority to Congress.
So, if the President is agreeing with Mexico and Canada to supersede US Law with regulations from the World Trade Organization and World Health Organization, isn't this a legislative act that requires the vote and approval of both houses of Congress or is it a Treaty requiring Senate approval? Can a President replace US Law with the law of a foreign body without Congressional approval at the very least?

Is it a coincidence that in 1776, the same year that the Continental Congress declared independence from England that Adam Smith published his book "The Wealth of Nations?" In the same year two experiments were introduced to the world, one political and the other economic. With the Constitution both experiments were set in law for a newborn nation. Do you know what these principles are and where they are set forth in the Constitution?
A nation's laws, rules and regulations can inhibit or promote the economy. We see clearly in our nation where certain federal laws can effect the prices of certain product and the ease of which a new venture may be begun. Our Founding Fathers were well read with Smith's book. They understood from England that a people could not be wholly free if they did not control their own resources of livelyhood, whether a person's resources included lands, materials, skills or simply the ability to perform manual labor. If a person or people did not have a say in what they could do with these resources they were as much slaves to the controllers of the resources as if they were politically slaves as well.
Smith gave us a conceptual definition of economic freedom that was upheld in our Constitution.
* 1. The Freedom to try.
* 2. The Freedom to buy.
* 3. The Freedom to sell.
* 4. The Freedom to fail.
How are these freedoms critical to economic and political freedom? Write and share how you think the two classes of freedom are linked.    

From the Federalist Papers
The two great points of difference between a democracy and a republic are: first, the delegation of the government, in the latter, to a small number of citizens elected by the rest; secondly, the greater number of citizens, and greater sphere of country, over which the latter may be extended.
The effect of the first difference is, on the one hand, to refine and enlarge the public views, by passing them through the medium of a chosen body of citizens, whose wisdom may best discern the true interest of their country, and whose patriotism and love of justice will be least likely to sacrifice it to temporary or partial considerations. Under such a regulation, it may well happen that the public voice, pronounced by the representatives of the people, will be more consonant to the public good than if pronounced by the people themselves, convened for the purpose. On the other hand, the effect may be inverted. Men of factious tempers, of local prejudices, or of sinister designs, may, by intrigue, by corruption, or by other means, first obtain the suffrages, and then betray the interests, of the people.
(The Federalist Papers, No. 10)

Selected grievences against the King listed in the Declaration of Independence

He has forbidden his governors to pass laws of immediate and pressing importance, unless suspended in their operation till his assent should be obtained; and when so suspended, he has utterly neglected to attend to them.

He has dissolved representative houses repeatedly, for opposing with manly firmness his invasions on the rights of the people.

He has obstructed the administration of justice, by refusing his assent to laws for establishing judiciary powers.

He has made judges dependent on his will alone, for the tenure of their offices, and the amount and payment of their salaries.

He has kept among us, in times of peace, standing armies without the consent of our legislature.

He has affected to render the military independent of and superior to civil power.

For quartering large bodies of armed troops among us:

For protecting them, by mock trial, from punishment for any murders which they should commit on the inhabitants of these states:

For cutting off our trade with all parts of the world:

For imposing taxes on us without our consent:

For depriving us in many cases, of the benefits of trial by jury:

For abolishing the free system of English laws in a neighboring province, establishing therein an arbitrary government, and enlarging its boundaries so as to render it at once an example and fit instrument for introducing the same absolute rule in these colonies:

For taking away our charters, abolishing our most valuable laws, and altering fundamentally the forms of our governments:

He has abdicated government here, by declaring us out of his protection and waging war against us.

He has plundered our seas, ravaged our coasts, burned our towns, and destroyed the lives of our people.

The basis of our political systems is the right of the people to make and to alter their constitutions of government. But the Constitution which at any time exists, till changed by an explicit and authentic act of the whole people, is sacredly obligatory upon all. The very idea of the power and the right of the people to establish government presupposes the duty of every individual to obey the established government.
George Washington's Farewell Address 1796

The procedure for changing the Constitution is set forth in Article V of the Constitution.

The Congress, whenever two thirds of both Houses shall deem it necessary, shall propose Amendments to this Constitution, or, on the Application of the Legislatures of two thirds of the several States, shall call a Convention for proposing Amendments, which, in either Case, shall be valid to all Intents and Purposes, as Part of this Constitution, when ratified by the Legislatures of three fourths of the several States, or by Conventions in three fourths thereof, as the one or the other Mode of Ratification may be proposed by the Congress;
(US Constitution, Article V)

If the Constitution is to be construed to mean what the majority at any given period in history wish the Constitution to mean, why a written Constitution?
(Frank J. Hogan)

Indeed, if the Constitution has no more meaning than what an elite group says it means than why did the Founding Fathers so painstakingly write the Constitution. Why not just establish some tribunal to decide?

But the Founding Fathers did intend and establish the Constitution as the SUPREME law of the land. (see Article VI of the US Constitution) They understood the nature of men and knew that when someone was in power, unless they were bound by something they could not violate, a person tended to become tyrannical. The Constitution as the SUPREME law of the land sets the foundation for all other law. It sets limits on what our federal government can and cannot do. It establishes a system of checks and balances in recognition of human nature to subdue the ability of someone to become a tyrant though it can never subdue that desire.

The Constitution is a contract with the American people and the states. Just as in a contract it establishes the rights and authorities of all parties involved. Just as in a contract it establishes how the contract can be changed or altered. As a contract it should be interpreted on the original intent. If all parties to the contract can agree on changes they can alter the contract in accourdance with the provisions provided in the contract, but one party does not have authority to make alterations without the formal consent of the others.

This contract grants authority to the government. And without this contract the government has no legitimate authority.

I acknowledge, in the ordinary course of government, that the exposition of the laws and Constitution devolves upon the judicial. But I beg to know upon what principle it can be contended that any one department draws from the Constitution greater powers than another in marking out the limits of the powers of the several departments.
James Madison, speech in the Congress of the United States, June 17, 1789

[The President] shall have Power, by and with the Advice and Consent of the Senate, to make Treaties, provided two thirds of the Senators present concur;
(US Constitution, Article II, Section 2, Clause 2)

The Constitution gives rolls to both the executive and legislative branches for the making of treaties. The rational for this was to provide a check on the treaty making process. By requiring a super majority of two-thirds in the Senate to agree to the treaty the Founders believed that more deliberation and thought would be put into the making of a treaty than common law. They also believed that by having the Senate consent to the treaty a small majority would be prevented from making treaties. (The smaller states had equal representation with the larger states in the Senate.) The House was too large in the minds of the Founders to be involved in making a treaty, this body would have difficulty keeping secrets or acting quickly.

The Congress shall have Power To lay and collect Taxes, Duties, Imposts and Excises, to pay the Debts and provide for the common Defence and general Welfare of the United States; but all Duties, Imposts and Excises shall be uniform throughout the United States;
To borrow Money on the credit of the United States;
To regulate Commerce with foreign Nations, and among the several States, and with the Indian Tribes;
To establish an uniform Rule of Naturalization, and uniform Laws on the subject of Bankruptcies throughout the United States;
To coin Money, regulate the Value thereof, and of foreign Coin, and fix the Standard of Weights and Measures;
To provide for the Punishment of counterfeiting the Securities and current Coin of the United States;
To establish Post Offices and post Roads;
To promote the Progress of Science and useful Arts, by securing for limited Times to Authors and Inventors the exclusive Right to their respective Writings and Discoveries;
To constitute Tribunals inferior to the supreme Court;
To define and punish Piracies and Felonies committed on the high Seas, and Offences against the Law of Nations;
To declare War, grant Letters of Marque and Reprisal, and make Rules concerning Captures on Land and Water;
To raise and support Armies, but no Appropriation of Money to that Use shall be for a longer Term than two Years;
To provide and maintain a Navy;
To make Rules for the Government and Regulation of the land and naval Forces;
To provide for calling forth the Militia to execute the Laws of the Union, suppress Insurrections and repel Invasions;
To provide for organizing, arming, and disciplining, the Militia, and for governing such Part of them as may be employed in the Service of the United States, reserving to the States respectively, the Appointment of the Officers, and the Authority of training the Militia according to the discipline prescribed by Congress;
To exercise exclusive Legislation in all Cases whatsoever, over such District (not exceeding ten Miles square) as may, by Cession of particular States, and the Acceptance of Congress, become the Seat of the Government of the United States, and to exercise like Authority over all Places purchased by the Consent of the Legislature of the State in which the Same shall be, for the <building> of Forts, Magazines, Arsenals, dock-Yards, and other needful Buildings; — And
To make all Laws which shall be necessary and proper for carrying into Execution the foregoing Powers, and all other Powers vested by this Constitution in the Government of the United States, or in any Department or Officer thereof.
(US Constitution, Article I, Section 8)

Here in this section of the Constitution we find what the original Constitution authorized the Congress to do. There has been a great deal of debate whether Congress was limited to what is authorized in this section or if the "general welfare" phrase authorized Congress to go beyond the limits of this section.

What is your opinion? Do you think Section 8 was originally intended to limit Congress to specific task?

On examining the first relation, it appears, on one hand, that the Constitution is to be founded on the assent and ratification of the people of America, given by deputies elected for the special purpose; but, on the other, that this assent and ratification is to be given by the people, not as individuals composing one entire nation, but as composing the distinct and independent States to which they respectively belong. It is to be the assent and ratification of the several States, derived from the supreme authority in each State, the authority of the people themselves. The act, therefore, establishing the Constitution, will not be a NATIONAL, but a FEDERAL act.
(James Madison, The Federalist Papers, No. 39)

To explain the term "federal act," the ratification of the Constitution was by not only the individual states but was also by the people of those states. A federal government is formed by a compact between political units (the states and the people of the states in this case) that surrender their individual sovereignty to a central authority but retain limited residuary powers of government.