Ms. Thompson, 22, whose husband also works at Jimmy John’s, said that they earned so little  she works just 12 hours a week  that her husband had joined the National Guard in part to bring in more money. One recent evening, after her car broke down, she asked her father to buy diapers for her 18-month-old because she was so financially stretched, she said.

One big complaint is how managers handle ill workers. When sandwich makers or delivery workers called in sick, several workers said, managers pressed them to find someone to take their shift. If they could not find a replacement, they were sometimes given a written reprimand. As a result, many employees have shown up to work while sick, the workers said.

Micah Buckley-Farlee, a bike delivery worker who earns $7.50 an hour plus several dollars an hour in tips, complained that management sometimes required workers to show up for three-hour lunch shifts, but then sent them home after 10 minutes or an hour when business was slow. Workers then were paid for just those short periods.

Mr. Buckley-Farlee, who has a collapsed lung condition, said that once when he felt a collapse was imminent, he called in sick and was told to find a replacement.

“I want a union for the little things  if you want a raise and the manager says no, you don’t have much redress,” he said. “And as for the big things like health coverage, you can’t get anywhere without a union.”

Mr. Mulligan said his franchise appeared to be the victim of left-wing activists who were looking for an employer to be a target. “This isn’t a situation where our employees decided they were treated unfairly and sought out union representation,” he said. He added that the Jimmy John’s activists include a veteran of the I.W.W.’s long effort to unionize Starbucks baristas.

Mr. Mulligan said he was an excellent employer who had hired many minority workers, promoted many workers into management and hired some ex-felons to help them get back on track. He said the fast-food industry was necessarily one of peak periods, part-time work and three-hour shifts. His company, he added, tells workers to stay home when they have the flu or another substantial illness.