Did it close the borders even for highly qualified workers "invited" by the companies? If no, is this so different than the U.S.?
Since the referendum was accepted (though with a really thin majority of 50.3 %) it will force Switzerland to renegotiate the treaty with the EU, which in fact already suspended further negotiations with Switzerland by itself.
Immigration of qualified workers will still be possible and encouraged by Switzerland, though. I think the main motivation behind the referendum was the fear of "Überfremdung" (foreign infiltration), which is probably not entirely irrational with currently 25 % of people living in Switzerland being of foreign origin. So I think one should not overreact here.
[1] https://www.bfm.admin.ch/content/bfm/en/home/themen/fza_schw...
[2] http://www.bsv.admin.ch/soziale_sicherheit/index.html?lang=e...