I have heard this argument before, but I think it misapplies the scripture in question, which speaks to crime, not full-scale, forthright revolution.
Romans 13
1 Everyone must submit himself to the governing authorities, for there is no authority except that which God has established. The authorities that exist have been established by God. 2 Consequently, he who rebels against the authority is rebelling against what God has instituted...
This may seem off-topic, but bear with me. The New Testament clearly establishes that believers are not to submit when asked to break the law of God. Peter sets forth this principle clearly in Acts 5. Christ, though, was the main example of this; and the church he established was illegal for much of it's early existence (and has been in various parts of the world ever since). As Paul was thoroughly familiar with this context, having been the persecutor and the persecutee, he clearly was not teaching a total, blind obedience to authority. But this applies to the American Revolutionaries only if Britain asked them to break God's law. Perhaps it may be argued that the Americans of the Revolutionary era would have acted in a cowardly, neglectful and unloving (and therefore antiscripural) way to their descendants, if they did not free themselves from British rule.
The main question is: What authorities has God established, and how? The American Revolutionaries believed that God placed sovereignty in the people, who instituted governments for their benefit and could "alter or abolish" their government as necessary.
That to secure these rights, Governments are instituted among Men, deriving their just powers from the consent of the governed, --That whenever any Form of Government becomes destructive of these ends, it is the Right of the People to alter or to abolish it, and to institute new Government
To them, apparently, God establishes authority by allowing the people to choose a ruler or regime. This would go a long way toward explaining the incompetence and cruelty governments have shown in the past few thousand years. It also comports with God's establishing a monarchy for Israel, even though He advised otherwise (1 Samuel
. Who is to say that God Himself did not act through the Revolution to establish the American nation and it's "authorities"? Does this unChristian Revolution argument make it a sin to overthrow Hitler, Tojo, the Taliban, or Saddam Hussein?
In sum, Romans 13 condemns individual acts of lawlessness for selfish reasons, not regime change.