NEW YORK — New York City is becoming the most populous place in the United States to make businesses provide workers with paid sick time, after lawmakers overrode a mayoral veto early today to pass a law expected to affect more than 1 million workers.

With the vote, the city joined Portland, Ore.; San Francisco; Seattle; Washington, D.C.; and the state of Connecticut in requiring the benefit for at least some workers.

Supporters see the New York measure as a pace-setter, although it has some significant limits and conditions, and they envision such laws becoming a national norm.

Advocates say workers shouldn’t have to choose between their physical and financial health. And customers and colleagues shouldn’t have to be exposed to employees who come to work sick.

But critics say that the government should leave sick day arrangements to workers and bosses.

Under the new law, 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.