As people of the Enlightenment, I would submit that this was less important to the Founders than liberty. They were well-aware of the blood that ran in the streets and battlefields of Europe secondary to the Reformation and Counter-Reformation (some of their ancestors left Europe because of this). They did not want those religious wars here and that is one reason why we have no state church and why they kept religion—though not God the Creator—out of our founding documents.
It has been my observation that many American Christians seem to identify their nation with the kingdom of God taught in the New Testament. The good ol’ US of A, however, is just that, a secular nation, not the kingdom of God.
The founders founded a secular nation, not a theocracy, not the kingdom of God. Neither were they devout Christians, as many seem to think, the main ones were Deists and Freemasons who believe there is a supreme being, but he is not the God of the Bible.
Using these Biblical passages from Romans, therefore, to try to make the Deist founders sinners is silly.