Way worse than Brexit, as Switzerland is much smaller, landlocked and had no colonies or anything like that. This would be a suicide for the country. Just populism to mobilize the electorate.
This is only about the Schengen, Switzerland is not a part of the EU, and even before the Schengen, the borders between the EU and Switzerland weren't heavily controlled. I got in trouble at German airport for going by train from Lausanne to Milan, and then plane to Berlin, I had no entry step into the Schengen because they didn't bother doing that on trains (pre-Schengen).
Everything else is negotiated under separate treaties. This would revert Switzerland to pre-Schengen, which is sad, but it wouldn't be suicidal.
how did they ever survive in the pre-EU/schengen/EEC era?
Imagine how crazy it is to call a population cap an act of "suicide."
Makes far more sense than the “population must increase forever” pyramid scheme the rest of the West is running. Check out Canada for a look at what happens when you try to juice GDP via population growth at the expense of literally everything else.