Jesus only asks you to voluntarily give that which is Ceasar's to. He never said Ceasar has the right to force it out of you.

So exactly what is Caesar's?

Taxation without representation is when the government forces you to pay for something you don't want, you didn't ask for, you don't support, and very often it is something you strongly oppose. For example, public education, social security, foreign wars and medicare.

So the money is only Caesar's if you voluntarily asked for the service agreeing to pay for the service in exchange.