I referenced the following article by Peter Lawler at Postmodern Conservative.
Here is a comment I left at that blog:
... I would add J. Adams in with Jefferson and Franklin. Adams may have been culturally more Calvinistic than the other two, but theologically he was at home with Jefferson and Franklin.
And the the latter two were not "deistic," but seemed to believe in a God every bit as "theistic" as John Adams'. The "Deists" of the day (Paine, et al.) did dig the term "Nature's God," so that point is valid. The DOI attempts to unite Deists, Unitarians and orthodox Christians, each of whom hold certain theological positions that contradict the other.
Those are the perils of America's Founding civil religion and trying to claim it for yourself. There is a little bit of it for everyone, and a little bit for no one.