Did you look at what resources were used in drafting the final product? Did you look at all the revisioning, etc., that lead to the final product. Just because a holy word isn't found a bunch of times in writings doesn't mean that they were not used in the formation of those writings.
Surely, someone has done the research. It's not as if the Constitution is a neglected item. Somewhere there's a book with a title like: "Scriptural Sources for the Clauses in the Constitution." Can you find such a book? Anywhere? As you read the Constitution, can you find the parts that have a scriptural source? Surely, if there were scriptural sources for the Constitution, this is known by someone other than you, and such an important bit of scholarship exists. But where is it?