Make up your mind! Either the founding fathers were influenced by their religious beliefs or not. You say there is nothing in regard to Christian thinking in our documents? I say everything from the bill of rights to the DOI shows Christian belief systems. Certainly they didn;t flow from atheism!
A complex subject. First, let's look at the history of political systems in Christendom before the American Revolution. All monarchies (the Swiss are an exception). All absolute monarchies too. There is nothing in the history of European nations -- or the bible -- that would serve as a model for the US Constitution. Put the bible and the Constitution side by side. Where do you find separation of powers? Where do you find the electoral college? Where (except Switzerland) is there a federal system such as ours was supposed to be? Where's the free press? Hey -- where's freedom of religion as we have it here? I could go on and on, but you will not find that our system of government is based on scripture. True, most of the founders were Christians, and all were excellent men. I readily grant that our Christian heritage contributed greatly in making their morality what it was; but they didn't create a theocracy, and they didn't make scripture our law.