The framers were mostly deist. Most saw Jesus as a wise man, but they didn't buy into any sort of divine revelations or miracles or magic or prophesy. Not the messiah, not the son of god. Just a very wise man.

Above all, they were pragmatist. Wisdom is only as useful as its application. They also believed that no god controlled the destiny of men, so it was their duty to control their own destiny. They were excellent examples of Enlightened men.

That's not to say America wasn't founded as a Christian nation. Most people were Christian, and the religion was the most in harmony with ideals of the Enlightenment.