In corporate conference rooms, such changes might be greeted with a yawn. After all, we professionals typically take paid sick leave for granted. But in today’s economy, where the fastest growing sectors are creating low-wage jobs, this change could not be more critical.

Blair Phoenix, 25, who earns $1,300 a month as a cook at Mr. Puri’s restaurant, found that out the hard way. When she was out sick for a week in March, she ended up with a $325 hole in her budget that she is still struggling to fill.

“It’s a relief,” Ms. Phoenix, a single mother, said of the new law. “It gives you room to breathe.”

The city’s Department of Consumer Affairs is spreading the word, hosting briefings for business owners and posting ads on subways, buses and bus shelters, and employers seem to be coming to terms with the new reality. Last week, there was so much interest in a briefing with city officials hosted by the New York City Hospitality Alliance that the group had to scramble to find a larger venue. (They expected 100 business owners; 200 showed up.)

As for Mr. Puri, 34, he felt anguished at first over the new law. In his sunlit restaurant, he and his employees often work shoulder-to-shoulder as they chatter about their weekends and favorite musicians while serving up vegetarian sandwiches and wraps.

He prides himself on being a progressive employer and pays his workers $10 an hour, $2 over the minimum wage. Even so, he acknowledges that his first reaction was: “Is this going to put me out of business?”

His concern faded when he learned that sick days only begin once a worker has been on the job for three months (current employees can start taking time three months after April 1). Then he crunched the numbers and realized that he could absorb the cost.

Mr. Puri still worries that some employees might try to take advantage of the new law. (“I guess I’ll have to cross that bridge when I get to it,” he said.) But as a former Wall Street analyst, he remembers how he counted on paid sick leave when he was an employee. His staff, he said, deserves the same.