But despite wavering support, the bill appeared as of Tuesday evening to have enough votes to pass narrowly. (Because two council members are absent for medical reasons, one will be on vacation and one seat is vacant, there are fewer votes up for grabs on Friday.)

“We’ve worked in good faith with the Teamsters and Council speaker to find the right approach, and we’re confident we’ll get it done,” said Wiley Norvell, a spokesman for the mayor’s office.

That has led those in opposition to ramp up their efforts in the last few days.

“We’re talking to everybody,” said John Samuelsen, the president of Transport Workers Union Local 100, which is seeking to organize the pedicab drivers. “And we’re targeting the ones that we think are going to vote with de Blasio on this terrifically concocted scheme.”

For Mr. de Blasio, the issue of horse carriages has been a yoke that he cannot seem to shed. Backed by money from wealthy advocates against New York City’s horse carriages during his 2013 mayoral campaign, he promised a total ban on his first day in office.

The mayor did not immediately deliver on his vow; polls and newspaper headlines indicated that his stance was unpopular. But he arrived at a compromise that preserved the industry and moved horses out of street traffic.

The bill came before a Council hearing last month, but the de Blasio administration struggled to answer basic questions, surprising some members who began to question their support for it. Last week, the administration moved to fill in the gaps with a “fact sheet” on the proposal sent to all members, including the price: about $25 million. Roughly 40 to 50 carriage driver jobs would be lost, the administration said.

Since the hearing last month, the city made several commitments to carriage drivers outside of the content of the bill, according to a union official with direct knowledge of the conversations and who was not authorized to discuss them publicly, including hack stands visible from park entrances and assistance from NYC & Company to promote the carriage industry.