A national ballot on an unprecedented far-right proposal to limit Switzerland’s population to 10 million concludes this weekend, amid warnings of devastating consequences for the country’s economy if voters back the initiative.

A “yes” vote would require the Swiss government to take steps to cap the population at 10 million by 2050, enacting tough restrictions on family reunification, residency permits and asylum if the number reaches 9.5 million before that date.

If the 10m threshold is still exceeded before 2050, the proposal by the far-right Swiss People’s party (SVP) would oblige the government to pull out of the country’s free movement agreement with the EU – ending its access to the bloc’s single market.

Switzerland’s system of direct democracy allows for “popular initiatives” that are put to a referendum if they get 100,000 backers within 18 months. Typically held four times a year, plebiscites are a long-favoured tool of the anti-immigration SVP.

Switzerland’s population has grown far faster than that of surrounding EU states, rising by 23% since the free movement agreement came into effect in 2002. Economic output has risen by about 24% over the same period, government figures show.

About 27% of Swiss residents are not citizens. Supporters of the “No to a Switzerland with 10 million” initiative say the influx of mainly EU workers puts housing, schools, transport, welfare and the Swiss way of life itself under unbearable strain.

“Uncontrolled immigration is causing Switzerland to grow far too quickly. The negative consequences are palpable in all areas of life,” the SVP, the largest party in Switzerland’s parliament since 1999, argued in its campaign.

The seven-member government, made up of ministers from Switzerland’s four biggest parties, including the SVP, is collectively against the initiative, warning it would threaten national stability, harm the economy and hurt Swiss prosperity.

Clear majorities in both houses of parliament have also recommended rejecting the proposal, as have the Swiss trade union federation, the Swiss Employers’ Association and Economiesuisse, the country’s main business umbrella organisation.

Rudolf Minsch, Economiesuisse’s chief economist, said the proposal was a populist attempt to fix complex problems with a simplistic artificial cap. “It sells the illusion of a free lunch, and will not solve our housing or traffic problems,” he said.

Thomas Matter, an SVP MP, dismissed the concerns as scaremongering. “We are not against immigration, but it has to be moderate and controlled,” he said. “Before, we had qualitative immigration; now we have quantitative immigration.”

Populist rightwing parties in Europe have successfully exploited – and inflamed – concerns over immigration, reflected in Britain’s 2016 Brexit vote and in surging support for parties such as France’s National Rally and the AfD in Germany.

However, while many nations limit immigration, no country has ever voted explicitly to cap its population, Philippe Wanner, an expert in demography at the University of Geneva, said – although countries such as China have legislated to reduce growth.

Like many European countries, Switzerland needs immigration because birthrates are falling and it faces a steadily ageing population, with the proportion of people aged over 65 due to climb to more than 27% from 21% by 2055.

Recent opinion polls suggest the campaign against the proposal has gained ground since the referendum was announced in February, but most surveys have pointed to a close race, with the “no” camp predicted to win with about 52% of the vote.

Polling stations will open briefly on Sunday to allow in-person votes, but up to 90% of voters in Swiss referendums typically vote by post. To pass, the initiative must win both the popular vote and a majority of Switzerland’s 23 full and six half cantons.

Results should be known by mid to late afternoon on Sunday.