CHICAGO (CBS) — The Chicago City Council has advanced Mayor Rahm Emanuel’s $7.8 billion budget plan toward a final vote next week, but they’re not done trying to make changes.

One sticking point has been the mayor’s plan to privatize the city’s 311 call service center.

Most aldermen seemed to worry if the city workers who man the call center are replaced by people unfamiliar with the city, requests for neighborhood services could be mishandled, and aldermen would be blamed.

Ald. Anthony Beale (9th) was among the aldermen who want that plan shelved, but he said it’s not dead yet.

“I think right now it’s still on life support, and hopefully we can pull the plug on it, and do away with the entire 311 issue that we’re dealing with,” he said.

Ald. Patrick O’Connor (40th), the mayor’s floor leader, said he understands the sentiment.

“It was a sticking point from day one. I think there were some union considerations that we’re taking into account, and some accommodations we’re trying to make with the bargaining unit that represents those folks,” he said.

Some aldermen and even a mayoral aide have said the privatization effort would be put on hold, but the mayor refused to go that far after Wednesday’s council meeting.

“I hear what members have to say. I’m not going to negotiate publicly,” he said.

The issue is who would or could pay for a $20 million to $30 million upgrade of the call center’s technology.

Aldermen also have been working toward an agreement with the Emanuel administration on a change to the proposed rule that would allow ride-sharing services like Uber to pick up passengers at the city’s airports, McCormick Place, and Navy Pier. They want those drivers to obtain chauffeur’s licenses professional taxi drivers already are required to have. They said that would even the playing field, and bring in new revenue for the city.