Since the government doesn't offer grants and scholarships to graduate students like it does for undergraduates, I don't think there will be much of an impact. For undergrads, cuts in government spending will result in higher tuition and there will be fewer spots---increased competition.
If you're asking how the debt crisis and an almost certain downgrade of US treasury bonds will affect the schools themselves--nobody can say because the US has never been downgraded. As Mohamed El-Erian put it, we would be in the land of uncertainty. However, I would venture to guess that a downgrade from AAA to AA would cause a spike in interest rates (~50-100 basis points) and people, corporations, organizations, and institutions like universities can lose a lot of paper wealth. Hence, I can see a downgrade indirectly affecting university research, rankings, and admissions by diminishing the value of university endowments.