Jesus is a master at answering questions with questions of His own. This is not just true in the Gospels, but in our lives as well. When we ask God for help or aid, often His response is a question: Is this truly the help that we need? Will what we have asked for truly be to our benefit? Are we just looking for our selfish desires? What effort have we put forth in this endeavor? Are we deserving of victory?
Jesus leads us to examine our lives, not to give us easy ways out of situations that we have brought upon ourselves. The Pharisees were able to quickly produce the Roman coin, indicating their own reliance upon it. They wanted to use the Roman monetary system without any of the responsibilities associated with it, trying to hide behind the Law of God. This is why Jesus calls them "hypocrites" before responding to their question.
We see this same sort of hypocrisy in our world today. People demand many things from our government without playing their own part as citizens. We look out for our own self-interests, and complain when they aren't met, when we aren't following Jesus's primary commandments: To love God (and thus His creation) with all our minds, all our hearts, and all our souls, and to love our neighbors as ourselves.