The First Amendment, along with most of the rest of the Bil of Rights, are applicable to state and local governments, and indeed, any "state actor" through legislation such as 42 USC s1983. This includes state-sponsored universities. Please feel free to look up the Incorporation Doctrine.
linumax writes: "One of the longest-running defenses of the hotly debated H-1B temporary worker visa program is that there are simply not enough U.S. workers to fill out many corporations' programming, engineering and back-office positions, leaving them no choice but to hire workers from overseas. eWeek reports that a new Senate bill takes this argument to task, demanding that employers make a "good faith" effort to hire a U.S. worker before bringing in a H-1B worker. It would require that employers prove not only that they tried and failed to hire a U.S. worker, but that hiring a foreigner would pose no cost advantage."