Let every soul be subject unto the higher powers. For there is no power but of God: the powers that be are ordained of God. Whosoever therefore resisteth the power, resisteth the ordinance of God: and they that resist shall receive to themselves damnation. 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 shalt have praise of the same: For he is the minister of God to thee for good. But if thou do that which is evil, be afraid; for he beareth not the sword in vain: for he is the minister of God, a revenger to execute wrath upon him that doeth evil. Wherefore ye must needs be subject, not only for wrath, but also for conscience sake. For for this cause pay ye tribute also: for they are God's ministers, attending continually upon this very thing. Render therefore to all their dues: tribute to whom tribute is due; custom to whom custom; fear to whom fear; honour to whom honour. - Romans 13:1-7
My experience and reading is perhaps not as broad as others, but, unless I am mistaken, I have not until recently run across the idea that these passages meant anything other than obedience to civil authority.
The immediate text itself appears to support this view.
1. The scope is not limited to Christians: Though the letter itself is written to Roman Christians, Paul states, "Let EVERY SOUL be subject unto the higher powers."
2. Government is authorized or appointed by God: "Whosoever therefore resisteth the power, resisteth the ordinance of God".
3. This authority spoken of bears the sword: "he beareth not the sword in vain".
4. This authority spoken of is an avenger or revenger: "...he is the minister of God, a revenger to execute wrath upon him that doeth evil." The little child of God is not an avenger, but waits on God to meet out justice: "Dearly beloved, avenge not yourselves, but rather give place unto wrath: for it is written, Vengeance is mine; I will repay, saith the Lord." (Romans 12:19)
5. This authority spoken of receives tribute or taxes: "For for this cause pay ye tribute also..." This harmonizes with Jesus' instructions in Matthew 22:17-21. The church and its officers are not a taxing entity.
Other verses that speak to the subject include:Titus 3:1,2 and I Peter 2:13-17.
Human government is a divine institution; anarchy is the realm of man. In Paul's thought in Romans 13, obedience hinges on two main things: the external consequences of disobedience and the internal conscience. I see no reason to doubt that Paul means the institution of human government which is ordained by God. There may be a wide range of opinions for practically applying this teaching, but are there any reasons to doubt this is the teaching?