many of the founding fathers were religious people (ben franklin not so much, and jefferson wrote his own version of the new testament that left out the miracles of Jesus because he didn't think much of them) and they drew from that in writing the constitution, but they did not specifically intend for us to be of one mind religiously. the pilgrims, otoh, or more accurately the puritans in new england, having fled their homelands because of religious intolerance, established their own communities here that were extremely intolerant of people who didn't want to follow their religious beliefs. it was reasonably common for them to expel people from their community who would not follow their religious beliefs.
we are a nation that has millions of Christians, but we are not specifically governed by religious principals. the immoral actions of congress and the president have established this over several years. the constant and blatant lying and dishonesty violate the ten commandments daily.