Chesterton wrote the America is the only nation founded on a creed. The founding documents have been often cited by people from other countries, liberals and conservatives. Many crucial things implied in other countries are explicitly referred to here. This is useful, for instance, with the Bill of Rights, which slows down destruction of liberties.
The Declaration of Independence was written mostly by Jefferson, who had little definite Christian faith, but incorporates the Natural Law.
As America gets increasingly secular, the founding documents have less and less authority anyway. The founders, who were not perfect men, did conscientiously try to prevent Tyranny. They never foresaw the power of concentrated Mass media, coordinating with secularized higher education.
But they succeeded for about two centuries to build a free nation compatible with Christianity. They should have eliminated slavery, they should have done other things too. But what they did, was good. For a long time.