Would Education tax credits starve the government?

I like the idea of education tax credits because a free market in education would be much better then the one-size-fits-all government system. But I wonder what would stop people (and businesses) from starving the government by everyone giving enough to scholarship so that they don't have to pay any taxes? People may choose to give money to an organization that supports their beliefs in preference to the federal government.

For more on education tax credits see http://www.cato-at-liberty.org/2007/05/11/loose-language-sinks-syllogisms/