Close, but no cee-gar.
It is a contract between the sovereign political subdivisions known as states and the centralized government sanctioned by the people.
The ONLY part of the Constitution that has anything to do with the people is the Bill of Rights, and that only enumerates a FEW of the rights that already exist.
It's WHY there was such disagreement on including the BOR to begin with.
Christianity is part of the Common, or Natural Law. Therefore it is Christianity that is the basis of our government. Religion of any other type is not synonymous with the American experience of Liberty!"
God . . . is the promulgator as well as the author of natural law.
Justice James Wilson, a signer of the Declaration, the Constitution, Original Justice on the U. S. Supreme Court, and the father of the first organized legal training in America.
"It is the duty as well as the privilege and interest for our Christian nation to select and prefer Christians to be their representatives, as this is a Christian republic -
Justice John Jay, Supreme Court Justice
I'll leave you with a quote taken from one of the writings used by the Founders to construct our government;
Of the Simplicity of Criminal Laws in different Governments
In republican governments, men are all equal; equal they are also in despotic governments: in the former, because they are everything; in the latter, because they are nothing.
THE SPIRIT OF LAWS Book VI By Charles de Secondat, Baron de Montesquieu
You wouldn't know a REPUBLIC if it jumped up[ & bit you on the butt!