NEW YORK - In a significant victory amid a push for paid sick time around the country, city lawmakers voted Wednesday to make businesses provide the benefit to an estimated one million workers who do not have it.

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. 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.

Supporters see paid sick time as a basic matter of working conditions, akin to a minimum wage, and a way to stop coughing, sneezing employees from spreading germs to their colleagues and customers.

Critics say some small enterprises can't afford the benefit, and businesses resent the implication that they are forcing ailing employees to come 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.

"These are sort of one-size-fits-all policies that don't work well in many industries," said Michael Saltsman of the Employment Policies Institute, a research group financed by foundations, businesses, and individual donors.

Employees of businesses with 20 or more workers would get up to five paid sick days a year beginning in April 2014; the benefit would kick in by October 2015 at enterprises with 15 to 19 workers. All others would have to provide five unpaid sick days per year, meaning that workers couldn't get fired for using those days.

Manufacturing companies would be exempt because they're struggling, City Council Speaker Christine Quinn said.