The result could be close, with the latest poll indicating 43 percent back the "Stop Mass Immigration" proposal and 50 percent oppose it.
Switzerland is not in the EU but is ringed by members of the 28-nation bloc, which is its main export market.
If passed, the proposal would bind the government to renegotiate within three years a deal which gives the EU's 500 million residents equal footing on the job market in this nation of 8.1 million people.
Opponents of the plan -- the government, most political parties and the business sector -- warn that ripping up free labour market rules for EU nationals in force since 2007 would unravel related economic deals.
"I urge the Swiss to vote with their heads and not from their guts," said Economy Minister Johann Schneider-Ammann.
The EU is already battling internal dissent over its own borderless labour market policy, which is often criticised in western Europe, and has ruled out any change in its deal with Switzerland.
"Switzerland can't just pick and choose," Viviane Reding, vice president of the EU's executive branch, told Swiss media.
She insisted free movement was part of a binding package of seven accords benefitting Switzerland and the EU alike -- some 430,000 Swiss live in EU countries, for example.
University of Geneva political scientist Pascal Sciarini said it was tough to forecast the vote result.
"If the Yes camp wins, there'll be total chaos and a huge period of uncertainty in relations with the EU," he told AFP.
The Yes coalition is unbowed, arguing that national sovereignty is at stake.
The referendum was the brainchild of the Swiss People's Party (SVP), the largest single force in parliament and known for campaigns taking aim at foreigners.
"Our initiative has only one goal: Switzerland has to be able to control the quantity and the quality of immigration again," SVP lawmaker Luzi Stamm told AFP.
"Uncontrollable immigration is always, and everywhere, a disadvantage for a wealthy country,"
'Playing with fire'
Referenda are the core of Switzerland's direct democracy, and the SVP mustered more than 135,000 signatures to force a vote.
Immigration and national identity have long been headline issues in a country with one of Europe's toughest laws on obtaining citizenship and a long tradition of drawing foreign workers into a wealthy economy with virtually full employment.
But over recent years, the proportion of foreigners has risen from around one-fifth of the population to almost a quarter.
The highest numbers of recent immigrants hailed from neighbouring Germany, Italy and France, as well as Portugal.
The proposal's supporters say the arrival of 80,000 new residents per year has been an economic and social disaster.
The campaigners allege that locals -- both Swiss and long-resident citizens of other countries -- have been undercut as EU nationals settle for jobs below their qualification level because it still means making a higher salary than at home.
Their hard-hitting billboards even blame foreigners' demand for housing for concreting over the landscape.
They also blame overpopulation for driving up rents and land prices, overburdening the health and education systems, and turning rail and road commuting into a nightmare of jam-packed trains and traffic lines.
They decline to say what they consider an acceptable level of immigration, but underline that around 40,000 immigrants entered the country each year before the financial crisis erupted in 2007.
Switzerland's business, industry, farm and hospital lobbies warn the plan would hit a swathe of key sectors relying on foreign labour and trade.
"This is playing with fire," Swiss Employers' Federation chief Valentin Vogt told AFP.
"If you have a headache, you don't operate on an artery," Vogt said.
"And that's basically what it is, because nobody knows what would come out of this."
Opponents also balk at reviving bureaucratic hurdles that previously applied before they could recruit a non-resident.
Vogt said Switzerland needs a steady stream of migrants to replace retiring workers in its ageing population.