I just found a great First Things article from 2003 discussing the faith of the founders.  It has this great quote, discussing how the founders viewed religion, esp. in light of the French Revolution.  Note the distinction between "natural rights" (human rights based solely on nature, without religion, as secularists want to do) and the alternative that we have, rights that come from God:

Coming from radically secular France, where the revolutionaries of 1789 seized, profaned, and closed Christian institutions throughout the republic in the name of “natural rights,” Maritain fears that Americans will not hold fast to their own originality:

Let me say, as the testimony of one who loves this country, that a European who comes to America is struck by the fact that the expression “separation between church and state,” which is in itself a misleading expression, does not have the same meaning here and in Europe. In Europe it means, or it meant, that complete isolation which derives from century-old misunderstandings and struggles, and which has produced most unfortunate results. Here it means, as a matter of fact, together with a refusal to grant any privilege to one religious denomination in preference to others and to have a state-established religion, <b>a distinction between the state and the churches which is compatible with good feeling and mutual cooperation. </b>  (emphasis added)

Also, I’m sure Islamists would love this one.  Read this  paragraph of the Virginia Declaration of Rights dealing with religion:

[We hold] that religion, or the duty which we owe to our Creator and the manner of discharging it, can be directed by only reason and conviction, <b>not by force or violence;</b> and therefore, all men are equally entitled to the free exercise of religion, according to the dictates of conscience; and that it is the mutual duty of all to practice Christian forbearance, love, and charity towards each other.
Note in the quote below, how the author addresses the claim that the founders were Deist – he says they used careful language in order to be inclusive, but they relied on Christian principles, and their generous use of broader generic terms was due to their Christian view that government should not be in the business of picking our religion.
While Madison’s use of the Christian tradition employs a restricted, even chaste use of theological language—the name Jesus Christ is never mentioned, only “divine Author of our religion”—there can be no doubt that his worldview is Christian. It is neither Kantian nor Hobbesian, Greek nor Roman nor Voltairean. Neither is it a full-blooded Thomist vision. Yet it embraces too many theological elements to be considered merely secular, philosophical, or unbelieving. It is neither rationalist nor relativist, and it is more than merely theist or, as the conventional jargon of historians puts it, “Deist.” In itself, while it does not affirm everything that orthodox Christian faith affirms, Madison’s vision is sufficiently impregnated with Christian faith to be not only unconvincing but even unintelligible without it.

Some may assert that although Madison’s formulations appear to be Christian, in reality they stand as typical Enlightenment philosophizing. But one has only to compare them to texts from Rousseau, Voltaire, and other secularist figures of the time to see how much Christian sentiment and metaphysics they embody in their simple, elegant statement of a man’s duties in spirit and truth to his Creator.

I think what most liberals hope for is Rousseau’s harmless civil religion, as discussed well by Joe at the evangelical outpost.  But this panacea is not true Xianity, nor is it really what our founders wanted as the interface of religion and politics.  Go read Joe’s article, it is his typical good stuff.