I've written fairly extensively on the subject of NASA funding (and the funding of state science in general), so I think I will let Murray Rothbard take this one:
How shall we finance our future explorations in space? The answer is simple: insofar as space explorations are a byproduct of needed military work (such as guided missiles) and only insofar, let the space exploration proceed on the same basis as any other military research. But, to the extent that it is not needed by the military, and is simply a romantic penchant for space exploration, then this penchant must take its chances, like everything, in the free market. It may seem exciting to engage in space exploration, but it is also enormously expensive, and wasteful of resources that could go into needed products to advance life on this earth. To the extent that voluntary funds are used in such endeavors, all well and good; but to tax private funds to engage in such ventures would be just another giant government boondoggle.