Well, you really don't have to dig very deep to realize we weren't founded on Christianity, per se. But we were definitely founded on a political philosophy that presupposed a strong moral and ethical social fabric rooted in Western thought, which is ethically dominated by Judeo-Christian values and cosmology (concept of reality). Most of the Founding Fathers were, in fact, various types of Christians in their religious backgrounds, but a few were atheists, a few key framers were Deists, a couple were Jewish, etc. Deists still basically believed in a Western concept of God. They just didn't believe he intervened in the lives of men or in nature. "The Great Clockmaker" is the phrase that gets used most often to explain Deism. He created it, wound it up, and then left it alone to run its course. Jefferson, the author of both the Declaration of Independence and the Constitution, was a Deist. But your point remains, however we refine the language.

You are indeed correct. When you rip any of the fundamental assumptions out of the equation of the American Experiment (as they called it), it begins to fail rather quickly. Several of the Founders wrote about these possibilities, too. Take an educated and informed electorate out of the equation and you have failure. Allow political parties to dominate governance and you have failure. Lose a strong moral fabric that keeps individual liberty restrained in its excesses and you have failure. They warned strongly against all of these, and we have raced down all three of these paths hell-bent for damnation.