If it wasn't enough that the Puritans were influenced by it, America's supreme law, the Constitution, is the incarnation of Martin Luther's doctrine of the Two Kingdoms, the idea that the religious and civil realms are, and should be, separate, which is, of course, an explication of Christ's command to "Give to Caesar what is Caesar's, and give to God what is God's."
How do we know this? James Madison, the Father of the Constitution declares it in an 1821 letter to F. L. Schaeffer:
It illustrates the excellence of a system [American Constitutional government] which, by a due distinction, to which the genius and courage of Luther led the way, between what is due to Caesar and what is due to God, best promotes the discharge of both obligations. The experience of the United States is a happy disproof of the error so long rooted in the unenlightened minds of well-meaning Christians, as well as the corrupt hearts of persecuting usurpers, that without a legal incorporation of religious and civil polity, neither could be supported. A mutual independence is found most friendly to practical Religion, to social harmony, and to political prosperity.