Question: What does it mean to say that the Constitution is a contract between the People and the States to establish a Federal Government?

A Contract, by George Sweeney

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.