The compromise reached on a sick-leave law for workers in New York City drew cheers on Friday from employees who have feared that catching a cold could cost them their jobs. But some employers complained that it would unfairly load yet another expense onto their shoulders.

The agreement would eventually require most businesses with at least 20 employees to provide up to five days a year off with pay for illness. It also calls for even the smallest businesses, like the bodegas found on nearly every block, to let workers take days off without pay but without jeopardizing their jobs when they are too sick to work.

Advocates for low-wage workers estimated that the plan would provide sick leave to more than 800,000 workers who do not now have it, while adding just 18 cents an hour in labor costs, on average, for each of them.

Employers like Paul Seres said the burden would be more significant than that.

Mr. Seres, a partner in a restaurant and lounge on the Lower East Side, estimated that paying his 50 employees when they are sick could cost up to as much as $16,000 a year. He assumed that his workers would take all of the days allowed, whether they were really ill or not, and that he would not be able to pass the cost on to his customers.

“When you serve food, every single penny counts,” said Mr. Seres, who operates Dinner on Ludlow, on Delancey Street.

The proposed law would cover part-time workers, as well as waiters and others who depend on tips. All workers would accrue one hour of sick pay for every 30 hours they work but would not be able to use it until they had been on the job for four months.

The agreement reached on Thursday calls for the law to apply to businesses with 20 or more employees starting in one year. In October 2015, the threshold would be lowered to 15 employees.

Manufacturing companies, which employ about 122,000 workers in the city, were excluded from the legislation because their industry was considered too fragile and because Connecticut excluded them from its sick-pay law, according to Christine C. Quinn, the speaker of the City Council.

Mr. Seres, who lobbied against the legislation, called the compromise “the best we could have achieved.” But he said he still hoped that a state law superseding the local one could be passed before the rules took effect.

“If it’s good enough for New York City, why wouldn’t it be good enough for other municipalities like Buffalo or Rochester?” Mr. Seres asked.

He said he hoped legislators in Albany would require that workers also contribute to a pool of money for sick pay that would be administered by the State Labor Department, as unemployment insurance is.

Workers like Luis Gonzalez who have gone to work while ill were relieved to hear that they might soon spend a day sick in bed without worrying about termination.

Mr. Gonzalez, a construction worker who lives in Queens, said he contracted the flu this winter but never missed a day of tearing down brick walls out of fear he might be fired.

“Many people in my community have suffered,” he said through an interpreter. “Either they cannot afford to take a day off without pay or they are moms who can’t stay at home to take care of their sick children.”

Lacking any allowance for illness, Mr. Gonzalez is in the same situation as about three of every five low-wage workers in the city, said Nancy Rankin, vice president for policy research and advocacy at the Community Service Society. In contrast, she said, fewer than one in five workers in the top quartile of wage earners in the city lacks paid sick leave.

Business groups, including the influential Partnership for New York City, opposed the sick-leave law until late this week, arguing that it would hurt small businesses and make the city less competitive. But some operators of small businesses said they already provided paid time off to sick employees and believed that all companies should do so.

Esmeralda Valencia [a member from Make the Road New York], who runs Esmeralda’s, an Ecuadorean seafood restaurant in the Bushwick section of Brooklyn, said she did not want any of her 10 employees to feel that they had to work if they were sick, especially if they might infect customers or fellow workers.

Time off for illness is a benefit that all workers deserve, whether their employers are large or very small, Ms. Valencia said.

“Our workers are not a machine; they are human beings,” she said. “They have the right to get sick at any moment.”

By Friday, when the Council appeared to have the votes to override an expected veto of the bill by Mayor Michael R. Bloomberg, even business leaders and Chamber of Commerce officials from Brooklyn and Queens who showed up agreed with Ms. Valencia.

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