What amazed the Pharisees and the Herodians about Jesus' response was how he refocused the issue to something much bigger than they had intended. In essence Jesus said, give Caesar what he has coming, a silver coin with his image on it. It's already his anyway, so let him have it back. But give back to God all that God deserves, which is everything, including yourselves.
If we are right about Jesus' intentions, then we must not try and develop a full-blown political theology from his words or use them to answer all the practical questions we may bring to the text. From this passage we cannot learn how or when to turn Christian convictions into public policy or how to vote in the next election. The fact of the matter is that Jesus did not say much about such things; and the rest of the New Testament provides different responses believers should have in response to human government. In Romans 13 Paul paints a positive picture of the role of government and commands Christians to obey it; but in Revelation 13 the author describes a government gone demonic and warns believers to resist it unto death. According to the book of Acts, it did not take Jesus' followers long to discover that "we must obey God rather than men" (Acts 5:29).
What we owe to God is infinitely more than we owe to Caesar. The Words of 1 Peter 2:17 help put the issue into perspective: Fear God, honor the king." There is a world of difference between those two obligations, no matter where we draw the line between God and the government. In the last resort, then, Caesar is Caesar, and God is God."