Robert Dale Owen on Romans 13:

This is perhaps the first notable example of a freethinker using the revolution/Romans 13 argument, claiming the Founding for anti-biblical principles. Plenty of devout Christians during the American Founding thought the revolution sinfully broke Romans 13. And for that and other reasons they remained loyalists.

As he writes:

In Paul's epistle to the Romans, the thirteenth chapter, at the first verse, we read: "Let every soul be subject to the higher powers; for there is no power but of God; the powers that be are ordained of God. Whosoever, therefore, resisteth the power, resisteth the ordinance of God; and they that resist shall receive to themselves damnation."

I know not what the private opinions of those sturdy patriots were, who, in the old Philadelphia State House, appended their signatures to the immortal document. But this I do know, that when they did so, it was in defiance of the Bible; it was in direct violation of the law of the New Testament. This I know, that, if deity be the author of the Christian scriptures, the signers of the declaration resisted the law, not of the King of England only, but of the God of heaven.

Needs it to remind you how emphatically the text quoted supports the conclusions thus drawn? "There is no power but of God." The power of George III., then, was of God. "He that resisteth the power resisteth the ordinance of God." The great scene on the fourth of July, then, was A Resisting Of God's OrdiNances. Jefferson, Franklin, John Adams, John Hancock, and all the rest, fought against God. George Washington led on his troops against God. Every revolutionary blow was directed against God's anointed; it was a blow aimed against the divine authority—an act of rebellion, subversive of the ordinances of God. Ay, let us not veil the truth! If a being who cannot lie penned the Bible, then George Washington and every soldier who drew sword in the republic's armies for liberty, expiate, at this moment, in hell-fire, the punishment of their ungodly strife! Then, too, John Hancock and every patriot whose name stands to America's Title Deed, have taken their places with the devil and his angels! All resisted the power; all, unless God lie, Have Received To THEMSELVES DAMNATION!

The text is plain as language can make it; the conclusions irresistible. For my own part, did I believe the Bible and hope to reach heaven, I should feel certain not to find one revolutionary soldier there. ...