Going public would be a seismic shift for a country whose health system is often hailed abroad as a model of efficiency, but is a growing source of frustration at home because of soaring costs.
"Over the past 20 years in Switzerland, health costs have grown 80 percent and insurance premiums 125 percent," ophthalmologist Michel Matter told AFP.
"This is not possible anymore. It has to change," said Matter, who heads the Geneva Physicians Association, which backs calls to scrap the current system.
Left-leaning parties have championed the push for a state-held insurance scheme, saying it is the only way to rein in rising premiums and guarantee they are used efficiently and transparently.
Sunday's referendum comes after reformers mustered more than the 100,000 signatures required to hold a popular vote, a regular feature of Switzerland's direct democracy.
Recent polls showed that 54 percent of voters oppose the plan.
In a sign of growing public concern, however, that is far narrower than the 71 percent who rejected similar reforms in a 2007 referendum.
The current system requires that every resident in the wealthy nation of eight million hold basic health insurance, but offers freedom of choice among the 61 companies competing for customers.
In a country where the average monthly net salary is 4,950 Swiss francs (€4,100, $5,268), health premiums are around 400 francs per adult per month.
That does not include out-of-pocket spending on treatment such as dental care, not covered by basic insurance.
Premiums vary by insurer, age and region of residence, and clients can cut them by opting for an annual deductible — a sum they pay from their own pockets — of up to 2,500 francs.
Critics say the current system is unfair because basic coverage costs a millionaire no more than it does a low-paid worker.
Studies show that almost one-fifth of those on low incomes have skipped at least one monthly payment in a country where rents and retail prices are among Europe's highest.
The reformers also allege that insurers have too much political clout, with research showing that 14 percent of lawmakers have links to health firms or the sector's lobby groups.
But for Switzerland's cross-party government and its right- and centre-dominated parliament, the current system has proven its mettle and is debt-free, unlike the health services of France, Italy or Britain.
"We don't have a deficit in Switzerland. It's a healthy system. Of course we can criticise a lack of transparency by some insurers, but state control isn't going to solve such problems," said Ivan Slatkine, a senior party official from the rightist Liberal Radicals.
Supporters of the status quo argue that higher premiums are inevitable given an ageing population and costly cutting-edge medical care, and say shifting to a public system would generate few savings.