Bryan Caplan has a characteristically brilliant post on the Swiss referendum. He links a tweet by Paul Haydon that shows that the areas with more immigration have been less supportive of closing borders.
One crucial point of the referendum is the following, as reported by the Telegraph:
Under the new proposals, employers will have to give preference to Swiss nationals and there will be quotas on the number of foreigners allowed in. That will include the many thousands of cross-border workers who live in France or Italy but work in Switzerland.
Employers will thus be "incentivised" to prioritise Swiss also over cross-border workers. If you look at the very map to which Bryan linked, you'll see that Canton Ticino, the Italian-speaking part of Switzerland, voted overwhelmingly in favour of the initiative: 68%. Canton Ticino has a large number of cross-borders workers (close to 1/3 of the active population) - and people sensed that it was attracting more and more, as Italy is sinking in its fiscal crisis.
Indeed: Switzerland is a small country with a comparatively high percentage of immigrants (27% of population vs 13% in the United Kingdom, for example). But people react there as they typically do to the immigration issue: they tend to consider wealth as a pie, and fear it might be sliced in smaller pieces. In a way, I think Switzerland in Europe today is in a unique position to attract highly skilled human capital from distressed economies. In this respect, quotas won't help.
However, I suspect the most interesting consequences of the Swiss referendum will be the unintended ones. The initiative was conceived to manufacture quotas against European immigrants, and the Swiss are already being bullied by European politicians, as the latter regard immigration quotas to be incompatible with the bilateral agreements that regulate the Swiss access to the common market. You should also not forget that Switzerland is currently negotiating tax-agreements with some European countries, including Italy and Germany. These agreements would purportedly mean the end of bank secrecy for Swiss non-residents. Is this whole process going to be slowed down by the referendum? How could the EU "retaliate"? Is a new phase of increasingly conflictual relationship between the Swiss and the EU opening? I do not think that skepticism towards the European Union was the prime reason why the Swiss voted as they did. However, I suspect that they might actually welcome a less friendly relationship with the EU, considering it necessary to preserve Swiss exceptionalism. Whether they would also be ready to endure the costs of such a policy, I won't speculate.