ST. PAUL — Minnesota’s Senate passed a bill that would extend 12 weeks of paid leave to new parents and sick workers, a top priority for Democrats this year that faces slim odds of becoming law due to Republican resistance.

Many large Minnesota companies already offer some form of paid leave, but Democrats who control the Senate say it’s inconsistent and leaves many families unable to take time off due to illness, caring for a sick family member or after having a child. Funded by a new tax on employers and worker income, the bill would set up a fund to replace lost wages for up to 12 weeks of leave starting in 2020. Businesses with less than 20 employees could opt out of the system.

“It’s important to think about the real impact it has on families in Minnesota,” said Sen. Katie Sieben, a Newport Democrat and chief architect of the proposal. “I know how challenging it was to return to work almost immediately after the birth of my third child.”

The paid leave policy is part of a broader bill that would also grant tax credits for college tuition bills, expand an existing tax break for lower-income residents to 110,000 more Minnesota families and exempt the state’s professional soccer franchise from property taxes for a planned St. Paul stadium. The full bill passed 37-29, with two Democrats joining all Republicans to vote against it.

House Republicans have shown little interest in pursuing the measure, deriding it as a payroll tax. They’ve similarly dismissed Gov. Mark Dayton’s more limited proposal earlier this year to offer six weeks of parental leave to the state government’s 35,000 employees.

It will figure heavily into negotiations in the session’s final weeks, as legislative leaders try to compromise on a plan to split the state’s $900 million surplus between transportation, tax cuts and other spending priorities. Senate Majority Leader Tom Bakk has repeatedly called passing a paid leave policy a marquee effort for the year as he and Democrats aim to retain control of the Senate.

Offering more generous leave to workers has been a rallying cry for Democrats across the nation as the election approaches. Presidential candidates Hillary Clinton and Bernie Sanders both have made a 12-week parental and medical leave policy a fixture in their stump speeches as they vie for the Democratic party’s nomination.

As the measure is crafted in Minnesota, workers would pay into the fund through a new income tax, from a 43 cent weekly fee on those earning $25,000 a year up to a $2 charge on people making a salary of $118,500. Employers would also pay into the fund, which would provide up to $1,000 in wages a week for those on leave. Three other states offer a similar policy, Sieben said.

GOP state senators didn’t object to the proposal outright, but said it needed improvements. Sen. Michelle Benson, R-Ham Lake, said it would unfairly punish small businesses that temporarily expand for a rush of business by levying the paid leave tax for an entire year once they’ve crossed the 20-employee threshold. Sen. Gary Dahms expressed concern that complying with the new leave system would saddle local school districts with big expenses.

“This is just going to pile on another cost,” the Redwood Falls Republican said. “You really don’t know what kind of peril this will put them in.”

Major business organizations like the Minnesota Chamber of Commerce fought the proposal, arguing that employers, many of which are already voluntarily offering paid leave to workers, are better suited to craft a system that works for them.