In the 1990s Princeton was thinking about getting rid of tuition altogether. They backed off on that, but an influx of poorer students might not hurt them that much.
This is a bit late, but yeah. Until 2009 or so, the few schools in the country with very, very large endowments (basically, Harvard, Yale, Princeton, and I think Stanford, maybe a couple other schools) had been faced with a problem -- their endowments were growing faster than they could spend the money and it was starting to threaten their non-profit, tax-exempt status. There was a very real possibility that they would have
to move to a tuition free system as a result. This is also what all the construction on those campuses was about. Princeton hired Frank Gehry to design their new biology library, for example, because they needed a money sink. From what I've been hearing, they're starting to see runaway growth again too, so we may see free tuition from these schools within the next 20 years.
The problem with this, incidentally, is that the amount of funding these schools have available puts tremendous pressure on everyone else to supply the same kind of facilities and financial aid without the same means. Well, that and that it leads them to make bad choices. The Gehry library is reportedly less than popular and I believe I've heard that it's already leaking.