UPMC officials say the company’s service employees, like cafeteria workers and janitors, are paid $12.81 an hour on average, which they say is above market for Pittsburgh and well above the $10.10 minimum wage President Obama is seeking.

Image Christoria Hughes, a food service worker for UPMC, says her income is “not enough to live in Pittsburgh.” Credit... Jeff Swensen for The New York Times

Christoria Hughes earns $12.85 an hour after six years as a food-service worker at UPMC Presbyterian Hospital. “That sounds good on paper, but when you bring it home, it’s less than $350 a week,” said Ms. Hughes, who has money deducted for health insurance and is helping to raise several granddaughters. “UPMC claims they pay everybody these fantastic wages. It’s not enough to live in Pittsburgh.”

Ms. Hughes was arrested in February as were 11 members of the clergy; they refused to leave UPMC’s headquarters, insisting on meeting with Jeffrey A. Romoff, the company’s chief executive.

“UPMC is a world-class medical facility, we’re asking them to strive to be world-class in their labor relations,” said one of those arrested, Rabbi Ronald Symons of Temple Sinai. “We know that you can’t raise a family on those wages.”

Other unions are backing the service employees. “It’s important that the labor community demonstrate to UPMC that this is still a union town,” said Leo W. Gerard, president of the United Steelworkers union.

The union-versus-UPMC battle sometimes seems less a traditional unionization battle than an experimental labor effort to demonize, irritate and embarrass the hospital system into adopting a $15-an-hour wage floor, up from the current $11. If UPMC adopts a $15 minimum, union officials say, it will become a model for Pittsburgh and other cities where hospitals are the largest employers.

UPMC officials are not shrinking from their fight with the union. “I expect very little from them and they exceed my expectations,” said Gregory K. Peaslee, UPMC’s senior vice president for human resources.