I wonder who told you we're a Christian nation? There are many subtle meanings in the phrase.
First, part of the point
of the First Amendment--the freedom of religion--is that we are not
a Christian nation, that we may worship howsoever we may choose, and if one wants to be a Muslim or Buddhist or make up one's own belief system out of thin air or what have you, no one's going to try and stop you. At least, that's the theory
behind the phrase.
You are right--many Enlightenment thinkers, of which our Founding Fathers may be included, were indeed Deists. They believed in God but disassociated themselves from the Church because, as they saw it, the Church, any Church, necessarily corrupted the true Word of God. I recall reading something about Jefferson's Bible; he basically compared all the sayings and doings of Jesus in all the four Gospels and extricated anything that all four didn't agree on (now we know, of course, that that might not have been the best way of going about finding out what Jesus actually said, but still...). I've heard a lot of rumors about Franklin's religious identity, and frankly, I'm from Philly, and I still find them a load of s...
Now, on the other side of the coin, is our popular religious identity. Although claiming religious nationhood violates not just the letter
of the Constitution, but the very spirit
of the Constitution as well, as a people we are, overwhelmingly, Christian; I think there are more practicing Christians here today, especially in the Deep South and the Midwest (the so-called Bible Belt) than in much more libertine Europe; for every single synagogue, mosque, or temple, I'll bet you you'll find ten churches. And of course there a great many distinct religious groups that call themselves Christians, as well: Eastern Orthodox, Catholic, Lutheran, Presbyterian, Baptist, Mormon, the list goes on and on, etc. etc. etc. So the bottom line is, in legal theory we are officially areligious, but in terms of what the people follow we are far more Christian than officially Christian European nations (like, e.g. Great Britain, where the monarch is the head of the Anglican Church).