Joe Carter has a very apt post on the Glenn Beck event and American Civil Religion. As he correctly points out, the idea of a more generic civil religion that purports to unite orthodox Christians with other religions under God and Country traces back to Rousseau.
Some readers/co-bloggers will disagree and try to save the civil religion under "Judeo-Christian" Providentialism, because, after all just about every citizen back then was a professing "Christian" of some sort even if some/many of them like "Christians" Jefferson, J. Adams and Franklin (yes, they understood themselves to be "Christians" not "Deists") didn't worship a Triune God, but a unitary one.
Yet, when it came time to dealing with the one group of non-Western, non-Judeo-Christian types -- the American Indians -- Washington, Jefferson and Madison repeatedly spoke of God as "The Great Spirit" suggesting un-converted Natives worshipped the same God Jews and Christians did.
J. Adams may well have too; I haven't yet found the evidence. But I have found letters of his where he, I kid you not, terms Hinduism and Zeus worship as "Christian principles."