WASHINGTON — 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 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 Barack 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. Similar initiatives also passed in the cities of Oakland, Calif., and Trenton and Montclair, N.J.

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 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 days 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, Ore., and San Diego passed paid sick days legislation, joining Portland, Ore., New York, Seattle, San Francisco, Washington, D.C., 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.