The requirement to obey government laws is based on the Book of Romans, chapter 13, where the Apostle Paul writes:
Let everyone be subject to the governing authorities, for there is no authority except that which God has established. The authorities that exist have been established by God. Consequently, whoever rebels against the authority is rebelling against what God has instituted, and those who do so will bring judgment on themselves. For rulers hold no terror for those who do right, but for those who do wrong. Do you want to be free from fear of the one in authority? Then do what is right and you will be commended. For the one in authority is God’s servant for your good. But if you do wrong, be afraid, for rulers do not bear the sword for no reason. They are God’s servants, agents of wrath to bring punishment on the wrongdoer. Therefore, it is necessary to submit to the authorities, not only because of possible punishment but also as a matter of conscience. This is also why you pay taxes, for the authorities are God’s servants, who give their full time to governing. Give to everyone what you owe them: If you owe taxes, pay taxes; if revenue, then revenue; if respect, then respect; if honor, then honor. (Romans 13:1-7, NIV)
Most Christians believe this to mean that Christians should, in general, submit to ruling authorities. Many would make an exception if governments ordered them to do things that were expressly contrary to the commands of God. And nothing in this passage says that governments always do the right thing, or prohibits attempting to change the mind of a government.
It is also supported by the example of Jesus in Matthew 17:24-28, where when asked if Jesus paid the half Shekel tax, Peter replied "yes", and in Matthew 22: 15-22, when the Pharisees sought to trap Jesus with the question about whether it was lawful to pay taxes to Caesar or not, and Jesus proclaimed that it was proper to render unto God what is God's and unto Caesar what is Caesar's.