NEW YORK — In a significant victory amid a push for paid sick time laws around the country, city lawmakers voted Wednesday to make businesses provide the benefit to an estimated 1 million workers who don't have it now.

Saying they hoped that requiring sick leave in the nation's largest metropolis would set an example, City Council members positioned New York to become the most populous place to approve such a law during a campaign that has scored several victories but also a number of defeats. A mayoral veto is expected, but so is an override.

Advocates see the measure as a signal accomplishment, although it has some significant limits and conditions.

"It's very important that it's happening in the biggest city," said Ellen Bravo, executive director of Family Values at Work, which promotes paid sick time initiatives around the country.

Supporters see paid sick time as a basic matter of working conditions, akin to minimum wage, and a way to stop coughing, sneezing employees from spreading germs to their colleagues and customers. The New York measure's sponsor, Councilwoman Gale Brewer, says it's about "a workplace that is safe, fair and respectful of the lives of workers."

Critics say some small enterprises can't afford the benefit and businesses resent the implication that they're forcing ailing employees to come in to work and creating a public health problem.

Government should let bosses and employees work out sick time arrangements on their own, they say. Some restaurants, for example, have shift-switching systems instead of paid time off, partly on the premise that servers would rather not lose out on tips.