Is All Power Legitimate?

In seeking to show that power must be justified in order to be legitimately exercised, one illustration that has been used is that of a grandparent who yanks his grandson by the arm, causing a moderate amount of pain to the boy. This is obviously an exercise of force that seems quite harsh, at least until we come to understand that the grandfather was pulling his grandson out of the way of an oncoming vehicle, thereby justifying the use of force. The moral of the story is that power is not always legitimate, but must be justified in order to be seen as such.

What, then, constitutes legitimate power or authority?

If it is wrong, as many argue, to employ armed resistance against a lawful government, even if it is oppressive, then what does that say about the American Revolution? And if we conclude that it was illegitimate for the Founding Fathers to take up the sword against the British crown, what does that say of the authority of our government today, over 200 years later?

Or take another example (one which was used in the comments under the previous thread): If China were to invade the U.S. and occupy this country, at what point, if any, should this new regime cease to be seen as illegitimate aggrressors and become legitimate recipients of our dutiful obedience and respect?

Is there a statute of limitations on rebellion? What if there are rival claims upon our obedience, as during the Civil War (err... excuse me: The "War of Northern Aggression")? Ought we simply fall back upon our own individual consciences to determine our answers to these questions?

And how can we maintain Christian unity amid the varying opinions that exist among believers on these issues?