A City Council hearing to address the budget for next year is scheduled for Tuesday morning, a day after a similar hearing ended up being called off due to the lack of a quorum.

Aldermen are scrambling to figure out how to pass a budget by the end of the month that can't be vetoed by Mayor Brandon Johnson. The back-and-forth between alderpeople and the mayor continues as the possibility of a city shutdown creeps closer.

A full City Council meeting and a hearing of the Finance Committee were on the agenda on Tuesday. Hearings have been scheduled every day this week through Thursday, as well as Tuesday, Dec. 23.

While the City Council meeting planned for Monday did not happen, the mayor did meet Monday afternoon with several members of a coalition opposed to his budget plan on Monday to discuss their latest counteroffer.

As the city faces a budget deficit of more than $1 billion, a key sticking point in budget talks remains the mayor's push to revive the city's corporate head tax, which would charge corporations a monthly fee per employee to fund youth violence prevention programs.

About an hour after their negotiations Monday, aldermen took a break and then didn't come back.

"We posed a simple question to the mayor — if we pose a budget with no head tax, will he veto it?" said Ald. Nicole Lee (11th). "We did not get a straight answer."

This was also the first time during the budget impasse that the mayor himself was at the table with aldermen, but Johnson said he was disappointed that they would not provide details of their plan.

"I never said that I would veto a budget that did not have a head tax in it. What I said was it really just depends on what they have proposed. But here's the problem, though — they literally withheld that information from me and my team," the mayor said. "Never in my life have I ever seen the level and the degree of obstinance coming from a legislative branch."

The group of the mayor's critics who oppose the head tax said Monday that support for their alternate budget plan is growing. Johnson's latest proposal for the head tax would charge businesses with 500 or more employees $33 per employee per month, but the mayor's opponents said any form of a head tax – which was eliminated in 2014 – is a no-go.

They devised a plan that would eliminate the mayor's head tax, but would have relied on increasing the city's garbage collection fee – which Johnson had vowed to veto.

On Monday, that opposition group of around two dozen aldermen said they had removed a higher garbage collection fee from their plan, but did not reveal how they would replace the estimated $35 million in revenue that plan would have created. Their alternate budget plan would also increase liquor taxes, expand a rideshare surcharge for Uber and Lyft, and improve debt collection by selling some outstanding debt to collection agencies.

"This package is a result of literally hundreds of hours of work and engagement from experts and more importantly with our colleagues, the majority of City Council," said Ald. Lee.  

The alders' latest alternative budget proposal also would maintain funding for youth jobs that the mayor had proposed in his original budget.

But Mayor Johnson said the math being used by the alders proposing the alternative budget does not add up.

CBS News Chicago is told more than half of the City Council supports the alternative budget. But at least seven ore votes are needed to avoid a mayoral veto.