At its headquarters in Basel, Swiss drugmaker Roche Holding employs workers from more than 100 countries. In less than a month, the access to international talent that it has long enjoyed could come under serious threat.

On June 14, Switzerland will vote on a plan to cap the population at 10 million. With the number already above 9.1 million, annual migration would have to drop by at least half to avoid reaching the ceiling by 2050, as proposed in the initiative. That would affect businesses from manufacturers to banks to tech firms, who have in recent decades brought hundreds of thousands of people into the country to fill jobs.

Roche’s chairman, Severin Schwan, has called it “dangerous for our society and for the economy.”

“Switzerland cannot meet the need for bright minds on its own,” he told shareholders earlier this year. “It’s vital to keep the borders open for top talent.”

Roche’s international workforce is a story repeated across the country.

In Zurich, Google employs more than 5,000 people from 85 countries. On the shores of Lake Geneva, Logitech International boss Hanneke Faber stresses the importance of international talent from the Swiss Federal Institute of Technology, which she calls the “MIT of Europe.”

But as Switzerland’s high wages and quality of life make it attractive for foreign workers, right-wing campaigners say the population growth is out of control. Voters are getting on board too. Polls show the electorate split down the middle, giving the proposal a realistic chance of passing.

Unlike anti-immigration campaigns seen in other European countries, the Swiss push doesn’t just target asylum seekers and refugees. It would also, if needed, bar high-earning bankers, scientists and engineers from entering the country.

The extreme idea has alarmed executives in Switzerland’s impressive roster of blue-chip firms. Novartis says reliable access to international talent is critical for businesses. For Nestle, the “free movement of skilled professionals from diverse backgrounds helps ensure that the country remains innovative and prosperous.”

The danger is not only a smaller labor pool but a rupture with the European Union, Switzerland’s biggest export market. The bloc’s principle of free movement underpins wider economic accords that ensure Swiss firms’ access to a $21 trillion economy and its 450 million consumers. Under the population proposal, Switzerland could ultimately have to terminate free movement agreements.

However, warnings about long-term economic fallout appear to be struggling to get through to voters who see long lines at apartment viewings, expensive rents and crowded trains that are affecting them right now. The cap appears to offer an easy fix, with a message that there’s just no more space for newcomers.

It’s even got traction among those who work for companies…