In the post-war period the US spent a decent chunk of money via mechanisms like state sponsorship of universities and the GI-bill to ensure that university education was accessible to most Americans.
All of that spending took a downward turn somewhere in the 80s & 90s. As a consequence students must bear the vast majority of the cost of their university education starting somewhere in the 00s.
Universities began looking elsewhere for other sources of funding (since you can't actually run a university solely on the backs of students), and began reaching out for grants from the US government (NIH and NSF being two major funders). Now that gridlock in the Congress has forced the sequester on all of our federal institutions, we're seeing research dollars take a dive now too.
Private schools are part of the problem, but the real problem is that American politics has abdicated its responsibility to educate its people.