I'm a big fan of Peter Lawler's "They Built Better Than They Knew" thesis about the American Founding, that they ended up with an "accidental Thomism" anyway, i.e., classical Aristotle/Aquinas natural law.
As I’ve said many times before, we can see that our Declaration was a statesmanlike legislative compromise between Lockeans and Calvinists, and the result was a kind of accidental Thomism. Something similar can be said about the actual language of the religion clauses of the First Amendment, which point in the direction, contrary to Madison’s theoretical anti-ecclesiasticism, of freedom of the church.
From John B. Kienker in First Things: "In a superb chapter on John Courtney Murray, Lawler defends the American founders' "implicitly Thomistic" liberalism (from which we've strayed), which, despite its debt to Locke, retained a conception of rights firmly grounded in natural law. Following Murray, he credits a Calvinist influence with tempering the founders' own liberal impulses, allowing them to build "better than they knew." He hopes that perhaps our politics may again experience a similarly fruitful tension between today's evangelicals and secularists."
More from Lawler here and here. Requiescat in pace.