Voters gave Republicans big wins in governor’s offices and shifted the balance of power in the Senate to the GOP in Tuesday’s midterm elections.

But here’s a twist: In several of those states, voters by large margins also passed initiatives to give workers paid sick days and to boost the minimum wage, issues that have long been associated with Democrats and have been central to President Obama’s domestic agenda.

A ballot initiative to give workers paid sick days passed in the state of Massachusetts — where Republican Charlie Baker narrowly beat Democrat Martha Coakley in the governor’s race —  making it the third state to pass a paid sick days law, after Connecticut and California. Initiatives also passed in the cities of Oakland, Calif., and Trenton and Montclair, New  Jersey.

The initiatives guarantee workers in companies with more than 10 employees one hour of paid sick time for every 30 hours worked. In Massachusetts, workers can earn up to to five paid sick days a year, and those who work for companies with fewer than 10 employees will be eligible for unpaid sick days.  In Trenton, it’s five paid sick days for companies with 10 or more employees and three paid sick days for workers in smaller companies.

In Oakland, workers in companies with more than 10 workers could be eligible for up to nine sick days a year, and, in smaller companies, up to five paid sick days. Oakland also voted to increase the minimum wage to $12.25 an hour. San Francisco, one of the first cities to pass a paid sick days law, also voted to boost its minimum wage to $15 an hour, putting it at the top of the pay scale in the nation, along with Seattle. Although California passed a statewide paid sick laws law in September, it grants workers only three days of paid sick leave a year.

Ellen Bravo, head of Family Values at Work, said that with Tuesday’s results, “so far, in 2014, we’ve tripled the number of locations with paid sick days and more than tripled the number of people covered.”

“This is really big. We have some real momentum now,” said Bravo, whose group has been seeking to pass paid sick days laws for more than a decade.

In July, the cities of Eugene, Oregon and San Diego passed paid sick days legislation, joining Portland, New York,  Seattle, San Francisco, Washington, DC., Newark, Jersey City and four other cities in New Jersey. Initiatives are pending in several other cities and states, Bravo said.

The United States is the only advanced economy without national laws requiring paid parental leave, vacation and sick days. Companies voluntarily may offer workers paid time off. As a result, about 40 percent of U.S. workers, many of them low-wage employees, have no paid sick days.

Workers like Gabrielle Montiero, 23, of New Bedford, a working-class area of Massachusetts, can be fired for staying home when they’re sick. Montiero, now a full-time student, was working at a laundromat a few years ago when she contracted pneumonia. Although she’d been in the emergency room until 3 a.m., her boss told her she had to find someone to cover her shift, or come in herself. Unable to swap shifts, Montiero came to work. But because she was late, she received a demerit, and was later fired.

“I couldn’t do much about it,” she said. So she started campaigning to change the law, going door to door, to pass the sick days initiative. “When I knocked on doors, people said they absolutely supported it. They’ve been in this position.”

Voters in four states that sent Republicans to the Senate, helping to tip the balance of power, also overwhelmingly passed ballot initiatives to raise the minimum wage, an issue that many political observers expected would draw Democratic voters to the polls.

In South Dakota and Nebraska, where voters elected Republican senators and governors, they also overwhelmingly passed initiatives to raise the minimum wage. The rate will go from $8 to $9 an hour in Nebraska and to $8.50, indexed to future inflation, in South Dakota.

Arkansans voted for Republican Tom Cotton for Senate, and also voted to boost the minimum wage from $6.25 an hour, which is currently lower than the federal minimum wage of $7.25, to $8.50 an hour over the next three years. In Alaska, voters picked Republican Dan Sullivan for Senate, and also, overwhelmingly chose to boost the state minimum wage from $7.75 and hour to $9.75 by 2016. In Alaska, more than two-thirds of the voters approved a hike in the minimum wage, which will be pegged to inflation.

Sullivan and Cotton said they opposed efforts in Congress to raise the minimum wage to $10.10 per hour, but, as polls showed strong support for state initiatives, both came to embrace the state efforts.

Business groups, largely in the low-wage restaurant and retail industries, fought these paid sick days and minimum wage proposals. Michael Saltsman, research director of the Employment Policies Institute, which is backed by the restaurant industry, said the initiatives have “unintended consequences.” He argued that the measures could result in higher prices to consumers, more low-cost automation, more burden on small employers and lost jobs.

“Sickness in the workplace is more of a public relations issue than an actual problem,” Saltsman said. “The vast majority of workplaces offer some type of paid time off policy. Others have schedule flexibility. It’s a status quo that’s been working quite fine.”

Not all business owners agree. Jerry Donovan, who owns a small construction and electrical contracting business in Fall River, Mass., has been an active campaigner for the paid sick days legislation.

“It is so exciting that the initiative passed, and passed overwhelmingly,” Donovan said on Wednesday. “The better you treat your employees, the more productivity you’re going to get, and the bottom line is going to be increased.”

Legislation to guarantee paid sick days and minimum wage hikes are extremely popular with voters. As many as 73 percent of voters surveyed by The Pew Research Center earlier this year favored raising the minimum wage. And 86 percent of those surveyed in recent years by the National Opinion Research Center at the University of Chicago favored legislation to guarantee workers paid sick days.

The state wins are in contrast to the inaction on working family issues at the national level. In his state of the Union Speech earlier this year, Obama called for an end to “Mad Man”-era policies that reflect an outdated world of breadwinner-homemaker families, and urged Congress to pass equal pay legislation, paid family leave, and paid sick days.

But with no movement on the Obama-backed Healthy Families Act – an initiative first proposed by the late Sen. Edward M. Kennedy in 2004 – advocates turned their attention to state and local jurisdictions. And they began to build broad coalitions of social justice groups, labor, the faith community and some businesses.

Deb Fastino, co-chair of Raise Up Massachusetts, said the coalition banded together more than 165 groups and 7,000 unpaid volunteers to pass the paid sick days initiative on Tuesday. In recent weeks, she said, the coalition gathered more than 360,00 signatures, made more than 350,000 phone calls and knocked on more than one million doors.

Advocates had been working with state legislators for years and got nowhere, Fastino said. “But then we took it into our own hands, and brought it directly to the voters,” she said. “That’s what made the difference this year.”