The technology and information involving space that actually helps human beings solve their problems would still be developed without NASA. Satellite communication companies come to mind.
The point is that as long as there is significant desire for something, a free market will result in people providing it to them as long as it is feasible. So if there are enough people that desire information about space exploration, a free market in the area would accommodate them. A free market would probably be even better than NASA, since there would be more competition, and resources would be put toward the research that would benefit people the most.
So in the end, I don't see the threat to space exploration and research if NASA is gone. It's important to a lot of people and a lot of businesses.
Do you think NASA does things that a free market wouldn't accomplish, and it's therefor right to fund it via forced taxation?