NEW YORK — The fight to redefine a McJob is heating up.

Protests for pay of $15 an hour and a union for fast-food and other low-wage workers are set to take place around the country today, marking the biggest effort yet in an ongoing campaign by labor organizers.

The push comes just two weeks after McDonald’s announced a pay bump for workers at its company-owned stores, suggesting the chain is trying to take control of its image as an employer.

The Fight for $15 campaign is being spearheaded by the Service Employees International Union and began in late 2012 with fast-food workers. Since then, organizers have used the spotlight to rally a variety of low-wage workers, including airport workers and home care workers. Adjunct professors will be the latest to join in the demonstrations today, which organizers say are planned for more than 230 U.S. cities and college campuses.

Kendall Fells, organizing director for Fight for $15, said McDonald’s will remain a focus of the protests because of its size and power to influence other employers. He dismissed the company’s pay bump as insignificant, but said it shows fast-food workers already have a de facto union.

“They were able to force the hand of McDonald’s,” Fells said. “They’re on the defensive, and workers are on the offensive. It shows the workers are winning.”

The first national pay policy announced by McDonald’s earlier this month includes a starting salary that’s $1 above the local minimum wage, as well as the ability to accrue paid time off. It only applies to workers at company-owned stores, however, which account for about 10 percent of more than 14,300 locations. That means McDonald’s is digging in its heels over a central issue for labor organizers: Whether it has the power to set wages at its franchised restaurants.

McDonald’s, Burger King and Wendy’s say they don’t control the employment decisions at franchised restaurants. That has long been seen as a roadblock to unionization, since organizers would have to negotiate with thousands of smaller employers, rather than a single company.

As part of the Fight for $15 push, the SEIU is working on multiple legal fronts to change that and get McDonald’s recognized as a joint employer at franchised restaurants.

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