Here at American Creation we've been meticulously studying and debating the meaning of texts of the writings of notable Founders. I realize appeal to authority is, technically speaking, an error in logic. However, if one is to appeal to an authoritative historian of American religious history, Mark Noll, of Notre Dame, (an evangelical by the way) is as authoritative as it gets.
Pages 31-32 in his 1990 book "Religion and American Politics" contain some interesting analysis. First he notes the Constitution was the 18th century equivalent of a "secular humanist text." Next he notes the delegates were not an orthodox group of men in any doctrinal sense. Noll states perhaps only ONE, Richard Bassett of Delaware, was a "born again Christian." Though Sherman "may" have been. Further, Noll notes Washington, Franklin, Hamilton, Madison, Wilson, and G. Morris gave no sign of belief in "original sin" at this phase in their life.
Noll then describes, using Jerry Falwell and Jimmy Swaggart as examples, how the Founders were actually closer to secular humanists than modern evangelicals (on a personal note, I'd say they were somewhere in between; they were "theistic humanists"). One ingredient of secular humanism is the willingness to elevate human reason over divine revelation when they appear to conflict. And Noll asserts that Jefferson and Adams clearly did this. He also notes by the 1780s Madison appeared to believe in "Nature's" Supreme Being as opposed to the God of Revelation. Finally Noll notes that James Wilson believed the Bible reinforced moral precepts, learned from reason and the moral sense, "not the other way around."
I've verified most of this independently through my own research. I've followed Gregg Frazer's lead who in turn heavy relies on and cites Noll's research in this thesis.
If the google preview shows those pages, I'd suggest reading them and as much of the preview that google books permits. This book is on my reading list.
UPDATE: Noll wasn't the author. John M. Murrin was. Noll edited. See here.