It doesn' matter what it pre-dates. If the founders recognized these as Christian principles, and acted on that recognition, then their actions were based on Christian principles.<quoted text>
Good luck with this one ...
I'm sorry, but I missed the Christian part there. That's the way a deist would write.
Incidentally, that phrase appears in the Declaration, not the Constitution.
Even if we stipulate that the god reference was sincere and not just rhetoric for hortatory purposes - it always helps to invoke a god to a religious audience - there is no mention of Jesus, Yahweh, or any other specific or named god, and no way to connect the ideas in the Constitution to the Christian bible.
And you're improvising with your mention of sin. The idea of members in a community supporting one another and punishing those in their midst that do harm is universal, and predates civilization, let alone Christianity.
You don't get the luxury of retroactive motive assignments.
"And can the liberties of a nation be thought secure if we have lost the only firm basis, a conviction in the minds of the people that these liberties are the gift of God? That they are not to be violated but with His wrath?"
-Thomas Jefferson, "Notes on the State of Virginia" (Philiadelphia; Matthew Carey, 1794), Query XVIII, p. 237
Sure sounds like a specific god.
This one gets even more specific:
"The practice of morality being necessary for the well-being of society, He has taken care to impress on our hearts that they shall not be effaced by the subtleties of our brain. We all agree in the obligation of the moral precepts of Jesus and nowhere will they be found delivered in greater purity than in his discourses".
-Thomas Jefferson, "The Writings of Thomas Jefferson, Albert Ellery Bergh, editor; Washington D.C., Vol. XII, p. 315, to James Fishback, September 27, 1809
Joseph Story, U.S. Supreme Court Justice; Father of American Jurisprudence:
"And, at all events, is is impossible for those who believe in the truth of Christianity as a Divine revelation, to doubt that it is the especial duty of GOVERNMENT <emphasis added> to foster and encourage it among all citizens and subjects. It yet remains a problem to be solved in human affairs whether any free government can be permanent where the public worship of God and the support of religion constitute no part of the policy or duty of the state in any assignable shape."