The amendments, which Council could vote on next week, would require businesses with 11 or more employees to let their workers earn seven sick days. Businesses with 10 or fewer employees would have to let workers accumulate four sick days.
The number of days was lowered from the original draft of the bill.
Other amendments would exclude interns, per-diem employees, and workers covered by labor contracts.
During public hearings, many business owners testified that sick days would amount to extra vacation days because no employee would leave them unused. Some employers threatened to leave the city if the bill passed.
"I respect businesses. We don't want businesses to leave the city," Greenlee said. "But I think they have to be reasonable and not just . . . doing Chicken Little all the time."
Mayor Nutter has said he opposes the bill, but he has not threatened to veto it.
"We praised the concept, the principle," Nutter spokesman Mark McDonald said. "But the legislation would be onerous for business, and particularly for small business."
Rob Wonderling, president and chief executive officer of the Greater Philadelphia Chamber of Commerce, said the amendments don't address the "overwhelming concerns" of small businesses.
"Although the goal of the proposed legislation is well-intentioned, this is clearly not the time to add another regulatory burden," he said.
A coalition of bill supporters, including ACTION United and a number of labor unions, have been staging events at City Hall for weeks. On Thursday, dozens of backers surrounded the building with a string of Day-Glo postcards from fellow supporters.
The coalition also released a poll this week that found that 71 percent of voters in the primary who responded were in favor of paid sick leave.
The bill, co-sponsored by Majority Whip Darrell L. Clarke, could come up for a final vote in two weeks.
Contact staff writer Troy Graham at 215-854-2730, email@example.com, or @troyjgraham on Twitter.