The correct interpretation of this passage is almost the exact opposite of the way most preachers and Christian laiety understand it.
"for rulers are not a terror to good works but to the evil wilt thou then not be afraid of the power do that which is good and thou wilt have praise of the same"
We see from verse 3 that the job of governments is to reward good and punish evil. Does that sound like manmade governments today?
Are criminals afraid of civil governments today? (v4)
Any civil government naturally needs taxes paid to it so it can perform its work, but Paul will go on to say in verse 8 "owe no man anything but to love one another." If I pay taxes I don't owe to fund policies that go against God's commandments, is that a loving action?
This passage is not telling Christians to kowtow down to manmade governments and obey every law they put in place. Indeed, such a thing would be physically impossible today.
Rather, this passage is meant for governing authorities themselves. Governments are put on earth to enforce God's law, rewarding good and punishing evil according to what God deems good and evil. When authorities step out of God's law, they are violating their purpose. Paul could not state it plainly this way for fear the letter would be intercepted by the Roman authorities.
When a government breaks God's law in any way, it ceases to be worthy of obedience.
"Well, no civil government can be perfect 100 percent of the time."
Exactly! That's why we have the law of God written in his word and on our hearts. When a government, even a well-meaning one, makes a law that violates the law of God, Christians should obey the perfect law of liberty over the manmade ordinance.
Think about it! Paul has just spent the previous chapters talking about the law of the spirit which brings life. He will go on in verse 9 of Chapter 13 to say that the whole law can be summed up in the commandment "thou shalt love thy neighbour as thyself." Why would he contradict himself by putting a passage in the middle of this discertation which says you should lick the boots of the civil authorities and do everything they tell you, even if it breaks God's law or was never part of His law in the first place?