America’s founders likewise, following Locke, were devout theists and gave God a prominent role in politics. See for instance, the Declaration of Independence. However, the God to whom America’s founders appealed — the individual rights granting Nature’s God — arguably was not the Biblical or Christian God. For one, the Biblical God does not grant men unalienable individual rights, certainly not a right to political liberty while the God of the American founding did. Further, on matters of religious toleration, the God of the American founding was not a “jealous” God but granted men an unalienable right to worship, in Jefferson’s words no God or twenty gods.
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. (For more on America’s founding creed, see this article.) 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.
There is, I think, a great deal to this line of argument. One doesn't have to share David Gelernter's triumphalism to think that there really is a politico-theological tradition, broadly defined, that one could reasonably call "Americanism" - a kitchen-sink mix of Providentialism, Deism, gnosticism, and Hegelianism that links the Founders to the Transcendentalists to the Progressives to Ronald Reagan and George W. Bush. And as Rowe points out, "the tension between America’s non-Christian, generally theistic civil religion, and orthodox Christianity does not so easily resolve." That's why if you scratch the surface of many nominal American Christians, you'll find that they really believe in the Osteen-ish tenets of moralistic therepeutic Deism, a faith that lines up more neatly with American political theology; it's why, as well, so many Christian patriots expend so much effort convincing themselves (but not many other people) that America was really founded as a bastion of orthodox Christian belief.
It's also why, like Andrew, I'm personally grateful that the American Constitution is an essentially secular document - not because it protects atheists from rampaging Christianists, but because it allows orthodox Christians like myself to be loyal to America's government without requiring us to accept, whole hog, the not-quite-Christian political theology that has infused American political life from the Declaration of Independence onward. That's the beauty of our Constitutional order: It allows one to be American without being an Americanist.