The following looks like a thoughtful blog by an orthodox Christian that well understands the tension between America's Founding civil religion and traditional biblical Christianity. It discusses among other things the dangers for traditional Christians in patriotism. Here is one of his posts on Romans 13 and the Nature's god [he purposefully has god in lowercase] of the Declaration of Independence.
The Declaration of Independence baptizes our nation into the name of a foreign god,and the founding fathers consciously dismiss the God revealed in the Bible. In the act of American independence, they defy a clear exhortation of the apostle Paul. Paul’s God does not impel revolutions. Paul’s God does not encourage His people to willfully rebel against appointed governors; even if those governors do not fear God. The god of Nature, however, does impel such actions. The fathers are entitled by Nature’s god to throw off English authority. How can we conclude that the founding fathers were following the same God as Paul?
I will gladly concede that traditional orthodox Christians can, in good faith argue over the compatibility of "Americanism" and "Christianity," and can reasonably conclude that yes, you can be both a good Christian and a good American. However, two points I want to stress: 1) The above quoted paragraph, without question, accurately represents a longstanding and reasonable, "literal" interpretation of Romans 13 in orthodox Christendom. And 2) whatever the compatibility between Americanism and Christianity, there was a very strong and profoundly influential non-Christian 18th Century Enlightenment-Whig worldview that influenced the Founding and orthodox Christians in the populace themselves.
Consider, whatever his faith, George Washington's favorite play, one he had played to his troops to rally them at Valley Forge was Cato about a figure from pagan antiquity who would rather commit suicide (yes, the very un-Christian act of suicide!) than submit to the political tyranny of Caesar.
No honest person can deny the tension between the pagan-worldview of "Cato the Younger" and that of traditional orthodox Christianity. That the American Whigs lauded Cato the Younger does not prove they were all non-Christians. Whatever Washington's faith, Patrick Henry, from what I've studied, was indeed an orthodox Christian. And he too lauded Cato. Indeed without that play the words "Give me liberty of give me death," probably would never have come from Henry's lips. The point is, even if those words were coming out of the mouth of a Christian the ideas were not biblical or Christian but pagan and Enlightenment. Again, we can debate the compatibility between Christianity and such Enlightenment-Whig ideas. But it seems to me, we cannot debate that "give me political liberty or give me death" is not an authentically Christian or biblical concept, but rather derives from a-biblical sources like Cato.
Cato likewise reflects the longing that the American Founders had for the non-biblical world of classical, Greco-Roman pagan antiquity. Both the Federalists and the Anti-Federalists adopted pagan, not biblical surnames. Hamilton, Madison, and Jay wrote the Federalist Papers, and all three of their faiths have been subject to debate. When writing the Papers it's likely that Hamilton and Madison were not orthodox Christians, but Jay (who only wrote 6 of the papers, compared to Hamilton's 52 and Madison's 28) was. Still that a Christian like Jay could write some of the Federalist Papers -- a series almost entirely devoid of biblical content -- using a pagan surname, "Publius," only further illustrates the tension between the worldview of the American Founding and that of traditional biblical Christianity.