There is in Switzerland the issue of low-skilled immigration. But arguably more problematic — from a Swiss point of view — is precisely the immigration which feels most Swiss, such as the professionals who come from Germany. Note that since the late 1990s Germans are the single largest group of immigrants coming to CH (pdf). The Swiss, of course, fear the European Union juggernaut as a mechanism for taking away their sovereignty. Having more Kosovars or more Sri Lankans in the country doesn’t strengthen the hand of the EU much. Those are not EU groups anyway, non-EU migration into Switzerland has been falling for a long time, and besides those groups can be excluded from mainstream Swiss society with relative ease, if need be. But German arrivals? Many would gladly see Switzerland join the EU and at the very least it feels like the decision is no longer under the control of the Swiss themselves. Furthermore they are not so different from German-speaking Swiss and they (sometimes) eat similar kinds of cheese. And because they are so often highly skilled, and can fit in so well, they cannot easily be excluded (pdf) from positions of influence in Swiss society.
In other words, sometimes it is the skilled arrivals the domestic citizenry wishes to limit in numbers. And you can see that the share of skilled immigrants has been increasing in Switzerland for years. Here are some recent percentages.
This study by Sandro Favre (pdf) shows that a major wage impact of EU migration into Switzerland has been to cut down high wages at the top of the Swiss wage distribution. So there is an economic motive too, and it is not the same story that is sometimes told about say southern California and Mexican competition with low-skilled American workers.
I, too, am a small country of sorts and I am glad I do not have thirty identical twins running around out there, competing against me or speaking on my behalf at meetings. I would wish to exile them to other planets.