Greenlee needs 12 votes for a veto override. So far 10 members have expressed support, and Greenlee said he is confident he'll get it through this time.
"It's fair to treat all workers with respect and provide decent working conditions," Greenlee said. "It's unfair, however, for over 180,000 workers in Philadelphia who can't just take a few paid days off to take care of their health or the health of their families."
The administration described the bill as commendable, but said it would hurt businesses and jobs.
"When imposed at a municipal level as opposed to a state or national level, [the bill] would create a significant disadvantage for Philadelphia businesses and the competitiveness of our city's economy," said Alan Greenberger, deputy mayor for economic development.
Greenlee grilled Greenberger and demanded to know why Donald Schwarz, the health commissioner, was not available to speak on the health aspects of the bill.
"Dr. Schwarz is an honorable man, and he would have come here and told the truth," Greenlee said. "That a big part of this issue is about the health of Philadelphians and the health of low-income workers, and to steal Jack Nicholson's line, 'You can't handle the truth.' "
Mayoral spokesman Mark McDonald said the administration thought Greenberger was the right person to speak on the bill.
Business leaders, including the Philadelphia Chamber of Commerce, said the measure would be too costly and would ultimately drive businesses out of the city.
A former city health commissioner, restaurant workers and some business owners that offer sick leave testified that the bill would benefit everyone and help prevent the spread of disease.
Under the bill, businesses with six to 20 workers would have to provide four sick days, and larger businesses would have to provide seven days. Mom-and-pop stores would be exempt. Interns, non-regular employees and state and federal employees would be excluded.
On Twitter: @Jan_Ransom