At American Creation we've done a great deal of discussion on St. Paul's Romans 13. But that's not the only proof text in the Bible that instructs believers to submit to and obey rulers. There is also 1 Peter 2:
13Submit yourselves to every ordinance of man for the Lord's sake: whether it be to the king, as supreme;
14Or unto governors, as unto them that are sent by him for the punishment of evildoers, and for the praise of them that do well.
15For so is the will of God, that with well doing ye may put to silence the ignorance of foolish men:
16As free, and not using your liberty for a cloke of maliciousness, but as the servants of God.
17Honour all men. Love the brotherhood. Fear God. Honour the king.
When it comes to proof texting the Bible, I don't see how anyone could dispute that the British had the more biblical argument; America's Founders did not "honour the king." What's a more interesting question is how Christendom, even orthodox Christendom, added a natural law that originates in Aristotle to the Bible as, at the very least, a supplement. Without that supplement, you don't get a right to rebel against tyrants.
Some argue that supplementing is a slippery slope to superseding; that might be true. But it is what America's Founders did. You don't get to rebel against a tyrannical King without looking outside the four corners of the Bible to "Nature."