New York City is poised to mandate that thousands of companies provide paid time off for sick employees, bolstering a national movement that has been resisted by wary business leaders.

A legislative compromise reached on Thursday night represents a raw display of political muscle by a coalition of labor unions and liberal activists who overcame fierce objections from New York’s business-minded mayor, Michael R. Bloomberg, and his allies in the corporate world.

The deal required a high-profile concession from a leading candidate to succeed Mr. Bloomberg, Christine C. Quinn, the City Council speaker, who had single-handedly blocked action on the sick-leave issue for three years, arguing that it would inflict damage on the city’s fragile economy.

The legislation would eventually force companies with at least 15 employees to give full-time workers five compensated days off a year when they are ill, a requirement that advocates said would allow much of the city’s labor force to stay home from work without fear of losing a day’s wage — or worse, a job. The advocates said the legislation would provide paid sick leave for one million New Yorkers who do not currently have such benefits.