Working parents gathered at City Hall Thursday to continue their push to extend sick leave to employees citywide.
They submitted 50,000 signatures asking the city to reopen a vote on the Paid Sick Time Act.
The bill would force businesses to give a number of sick days to most of their workers.
Parents said the policy would prevent employees from having to choose between their health and their jobs.
"Some days, you're sick and you have a headache and you can't always come in and come with a smile," said one working parent. "Sometimes you need that time off to gather yourself."
"You should never have to make that choice," said another. "As a mother, you should never have to choose between your job and your child's health."
City Council Speaker Christine Quinn and Mayor Michael Bloomberg have spoken out against a mandatory sick leave policy.
They said it would put an unfair burden on small businesses.