As someone who argues vociferously against accomodationists and JerUSAlemists, I do want to point out that there are a lot of laws and governmental practices which were rooted in Christianity that came out of the founding period and many which lasted for (IMO) far too long afterwards. Blue laws, which generally are ignored with the exception of alcohol sales in some states came out of Christian tradition. Of course even in Texas, where I cannot purchase alcohol (beer and wine until 1am Sat. and after noon Sun.), there are 24 hour adult video stores where I can purchase pornography.
Most state Constitutions (again, like Texas f.ex.) which have not overturned their Supreme Being conditions for office have at least a "wink wink, nod nod" approach to applying Article VI through the 14th Amendment for some sort of religious belief. Even then, look at what Kennedy faced in 1960, what Romney, were it not for his talk radio vanguard faced today and all the rumors and innuendo about Obama being a stealth Muslim. No federal or state entity would dare ask what religion a candidate for employment was because of VI/14, but the Christian influence of the culture is still effecting our politics.
When it comes to the federal Constitution, it's clear that the testimony of two witnesses (see the section on treason) came from the Bible. Another influence from the Presbyterian founders can (it seems) be found in the choice of elders being able to hold elected offices of higher and higher influence (rep. v. sen. v. pres.).
The founders were well versed in the Bible, the Classics and Enlightenment thinkers like John Locke. That is why this nation was not "founded on the Bible" nor purely the product of the Enlightenment, but the best kernels of political and social thought selected from 2,500 years of human experiment. "WE THE PEOPLE", not God or the God chosen king, did ordain and establish that Constitution in 1789 and included two witnesses being required for a charge of treason, one man/one vote*, a body of elder statesmen being the filter for legislation, an elected head of state and government, plus things like public buildings having columns and statues to conceptual deities (justice, columbia, etc.) and the concept of universal rights of concience, expression and enfranchisement*.
* It would take until 1920 for the two asterisked points to be enacted, but they eventually were.