The writings of the Enlightenment were the main philosophical guide of the Constitution, not the Bible. I have no doubt that each of the Framers paid lip service to it, because even today, not paying lip service to God is considered verboten (e.g.
every televised presidential speech ends in some version of "God bless"). But to claim that religion is a guiding principle of any Free state is simply wrong. We often hear conservatives talk about how the 10 commandments are the basis of our legal system. Anyone who asserts this has either never read the 10 commandments or is unfamiliar with the laws of the US. The only laws that appear in both regard killing and stealing, and are we to assume that without the Sacred Tablets that we would all be murderous larcenists? No, of course not. Those are rules that any functioning society must live by to maintain civil order.
I think one thing that Christians and non-Christians can agree on (albeit for vastly different reasons) is that the Bible isn't rational. The Constitution, on the other hand, is hyper rational and was created through trial-and-error and a series of negotiated compromises. To suggest otherwise, based on a few select quotes about the nature of morality, several of which don't even contain reference to any sort of divinity, is incorrect revisionist history. We could each also post disparaging things that were said by the Founders in regard to Christianity, but that would be fighting fire with fire, so I will not do that. The fact that we can debate what morality even is is sufficient evidence that it is derived solely from critically thinking people.