The Federalist Papers were an explanation of the Constitution - a lobbying effort to get the states to endorse the Constitution - as I am sure you know.
While the Constitution does not cite Biblical quotations, it is certainly based upon the Judeo/Christian culture, history, experience, education and beliefs of the Framers. They were almost all quite religious men. Many went to Church regularly at Christ Church while they were in Philadelphia.
I can't think of one who would have considered himself a athiest or an agnostic. I can't think of one who disavowed the Judeo/Christian concept of G-d.
So, whilst it would be wrong to say that the Constitution is "based" upon the Bible - it think it would correct to say that the precepts of the Bible formed the basis for the framing of the Constitution.
That is a good explanation, thank you.