Steve Scott has covered this as well as anyone http://fromthepew.blogspot.com/search/label/Re-Thinking%20Romans%2013, but I feel a need to rant about Romans 13 and other Biblical references to obeying authority. In my opinion, the authors of these texts were giving good advice to the early churches: Don't stand out as overtly seditious or as scofflaws. This made a lot of sense when persecution was a real possibility. It also made the movement unattractive to seekers who would fear to be associated with a gang of lawbreakers.
Beyond that, I reckon too much is read into the texts. They are qualified as holding that God ordains authorities to punish evil and reward good, and we all know that authorities go way beyond that mandate and even do the opposite. I suspect that this language was put in letters in case they were intercepted and that this was a kind of code for advising the assembly to avoid trouble and to appear to be loyal to rulers and, in fact, to pray for rulers and accept it if by chance they did something right. Any other reading seems absurd to me.
What is meant by authority, anyway? If Caesar conquers my country by the sword and exercises power over me, does he likewise have authority as from God? If we are never to rebel against authority, was not the founding of the United States via treason and rebellion a sin? And what of the simple subject of the crown in that rebellion? With whom was he to side? At what point is he supposed to recognize a new authority even when it is conceived in rebellion? Were the conspirators in the Underground Railroad sinners against God? What happens when one authority opposes another as in a war? Is God fighting God? Were the martyrs of the early church defying God when they defied Caesar?
I reckon the authors of these texts were stating nothing but the obvious when they observed that all authority comes from God. Since everything that happens from the beginning of time was foreordained, political events and figures were also foreordained just like plagues and hurricanes and mass extinctions. I reckon that the early Christians would have understood that but that outsiders would not have. Caesar's agents would have been able to report that Christians acknowledge Caesar's authority as Divinely Ordained. Caesar, having no discernment, might take comfort in that and, being a self important douche, would consider that it meant he was singled out. Of course, there was no pleasing Caesar, and it wasn't enough to declare him God's gift; you had to recognize him as God incarnate.
Read so as to avoid absurd implications, these texts are still good advice to Christians. Acquiesce in the requirements of rulers and avoid trouble as much as you can. It is error to read these texts as requiring blind obedience, let alone wholehearted acceptance and participation in the acts of governments.