By printing more money, he government has more money. By increasing the supply of money, the "price" (which is to say "value" - how much you can trade it for) of money goes down. So value moved from "those who hold dollars" to the government, which can be viewed as a sort of tax. By not using dollars, you reduce demand for dollars (hopefully more than you reduce supply through decreased velocity - see http://en.wikipedia.org/wiki/Velocity_of_money) meaning the government has to print more to pay for the same things and so you lessen the ability to raise money in this way.

I am skeptical about this being significant, because the amount of money raised by printing money has historically been radically lower than the amount of money raised by levying taxes.