One might imagine that the New Testament, much written under extreme religious persecution and a Roman emperor who called himself "the son of God," would encourage political resistance at every turn. This is not the case.
We need to temper the directions in the following passages about governmental compliance with the bedrock principle that a Christian's first allegiance is to God. When commanded not to talk about Jesus by Jewish leaders in Acts 5, Peter insists that "we must obey God rather than men." Obedience to God's commands supersedes all else. When a government demands that citizens commit evil, it's a Christian's duty to resist and protest. That said, when writing to the socially and politically persecuted church of Asia Minor in 1 Peter chapter 2, Peter is adamant that Christians should be known as law-abiding and peace-loving citizens:
13 Be subject for the Lord’s sake to every human institution, whether it be to the emperor as supreme, 14 or to governors as sent by him to punish those who do evil and to praise those who do good. 15 For this is the will of God, that by doing good you should put to silence the ignorance of foolish people. 16 Live as people who are free, not using your freedom as a cover-up for evil, but living as servants of God. 17 Honor everyone. Love the brotherhood. Fear God. Honor the emperor.
Paul makes a similar statement, arguing in Romans 7 that it's out of conscience and submission to God that we pay taxes and respect authority.
13 Let every person be subject to the governing authorities. For there is no authority except from God, and those that exist have been instituted by God. 2 Therefore whoever resists the authorities resists what God has appointed, and those who resist will incur judgment. 3 For rulers are not a terror to good conduct, but to bad. Would you have no fear of the one who is in authority? Then do what is good, and you will receive his approval, 4 for he is God’s servant for your good. But if you do wrong, be afraid, for he does not bear the sword in vain. For he is the servant of God, an avenger who carries out God’s wrath on the wrongdoer. 5 Therefore one must be in subjection, not only to avoid God’s wrath but also for the sake of conscience. 6 For because of this you also pay taxes, for the authorities are ministers of God, attending to this very thing. 7 Pay to all what is owed to them: taxes to whom taxes are owed, revenue to whom revenue is owed, respect to whom respect is owed, honor to whom honor is owed.
The Bible is full of examples of people resisting the government to prevent murder and genocide. The book of Daniel records two instances of civil disobedience by captive Jews in Babylon, shunning idol worship and religious compromise at the penalty of capital punishment. The Bible seems to indicate that though we have a duty to resist evil from our government, the legal consequences are ours to bear as well.