Anyway, here is an excerpt from my article:
In studying their public and private writings in detail I have concluded that America’s principle founders (Washington, Adams, Jefferson, Madison, and Franklin) were not closet atheists but really did believe in this rational, benevolent, unitarian deity who fit their republican ideals much better than the Biblical God could. The inescapable conclusion is that America does have a political theology; it is just not Christianity....Nature’s God was theologically unitarian, universalist (did not eternally damn anyone) syncretist (most or all world religions worshipped Him), partially inspired the Christian Scriptures, and man’s reason was ultimate device for understanding Him. He was not quite the strict Deist God that some secular scholars have made Him out to be. But neither was He the Biblical God. Rather, somewhere in between.
The political-theological problem America’s founders thus faced is they needed to and did appeal to a God that orthodox Christians did not worship. Such Christianity was socially and institutionally entrenched at the state level during America’s founding era. Though, some studies have shown huge portions of the American populace during the founding era were nominal or unchurched Christians. When the first four Presidents invoked this God in their public supplications, they systematically used generic or philosophical terms for God so as not to contradict either their heterodox opinions on God or the orthodox opinions of the masses (or least the churches to which the masses belonged). In doing so, they established America’s civil religion.