I want to thank everyone for the links and discussion to my post on enlightening Christianity and Islam. First Ed; then Chris Ho-Stuart, then PZ Meyers; and finally Andrew Sullivan. Also see Jason's and others.
PZ notes something that should be stressed: Even though the US, revolutionary for its time, disestablished religion at the national level when founded, other liberal democracies retained their established Churches which likewise enlightened. Indeed, Western Europe and its established Christian Churches became even more liberal and secular. He writes:
I'll add, though, that other countries did set up state religions, and then seem to have modified that institution into similarly benign forms that have had a more lasting effect. The unofficial position of America's founding fathers may have been wonderfully positive in the beginning, but we can see now that they flopped mightily at building enduring institutions that would maintain any kind of religious rationalism. I tend to think that if they had, for instance, declared Unitarianism the official US religion (with the same strong statements that religion was not to be a prerequisite for holding office, etc., and that it was not a declaration of exclusivity) we'd be better off today. There'd at least be one officially sanctioned brake on the excesses of our wildly proliferating looney-tunes churches.
Based on my meticulous study of Jefferson, Adams, and Franklin, they probably desired Unitarianism as the "official" religion of the US. The same thing, however, that prevented the Founders from abolishing slavery in the original Constitution, prevented this desire -- the states would never have ratified the Constitution were this to be done. Though, the Founders may have secretly intended to "de-facto" establish unitarianism or "theistic rationalism" as the US's Founding creed.
The US Constitution makes no mention of God, Christ, or Christianity and only recognizes "religion" in terms of granting it rights (free exercise) and imposing restrictions (i.e., no establishment or religious tests) which ultimately relate to securing the unalienable rights of conscience. If any kind of creed can be gleaned from the US Constitution, it is latitudinarianism. Arguably though, no creed can be gleaned at all.
While we have a "godless" Constitution, based on other founding documents, (the Declaration et al.) and the public supplications and privately recorded beliefs of our key Founding Fathers, they did believe America to be a nation "under God." However, as I've noted many times, such conception of a "civil religion" or "public creed" for the United States isn't, or arguably isn't Christianity, but a form of theological unitarianism which Dr. Gregg Frazer has dubbed "theistic rationalism."
The responses which atheists (who don't like any conception of God), or conservative Christians (who don't care for "unitarianism") can invoke is that we aren't governed by the secret intentions of our Founding Fathers but the original public meaning of the text of the Constitution. And the Constitution a) is Godless (something atheists will point out), and b) allowed the states to establish and promote Christianity over other world religions or non-belief (something conservative Christians will point out).
Still, ideas have consequences. The fact that America is a religiously pluralistic nation which still favors religious oaths in courts of law but guarantees its citizens the right to use "any religious text, not just the Bible," directly traces back to our Founding Fathers' widely latitudinarian religious ideals.