Wow. The amount of quasi-xenophobic comments in this tread is nuts. They are also a bit misguided.

You don't hire a professor at a R1 school just to teach math101. You hire them they can build a research lab or otherwise help to advance the frontier of the field (cancer, stats, etc.). The talent pool in several of these fields is very very small for Americans, because the brightest just go (used to go?) to work to finance or tech. So if you say you can't bring any bright foreigners, you are constraining yourself to a lower talent pool than other countries, and thus will pay a price (in less research, in no foreign students applying and thus no $$ from them, etc etc)