Let me refer you to this article addressing this very subject. As Mr. Cherry states, our Founding Fathers, whether Christian or Deist, did believe in God, and that our rights as men are given to us by God, and not by government. Add to this the fact that all of them grew up in the Christian tradition, as opposed to say, a Hindu tradition, and it is easy to see that our national identity arises from Judeo-Christian values.
Nevertheless, the Founding Fathers understood that there is a power greater than Man, upon whom man is dependent for liberty and morality. Tocqueville (yes, him again) remarked on the religiosity of Americans and the importance of religion in democracy, echoing, as it were, John Adams:
""We have no government armed with power capable of contending with human
passions unbridled by morality and religion. Avarice, ambition, revenge,
or gallantry would break the strongest cords of our Constitution as a whale goes
through a net. Our Constitution was made for a moral and religious
people. It is wholly inadequate to the government of any other.""
It is no surprise, then, that the immoral and irreligious Left continually try to distort the Constitution or ignore it altogether.