Some alders who are against the tax claim they can find savings within City Hall that will make up for the $100 million the mayor says the head tax will generate.
"There's no way you're going to get to that number unless you're committed to laying people off and firing law enforcement. I'm not going to do that," Johnson said on Wednesday.
Some alders are confident they can get to the number without layoffs through efficiency across 30 city departments.
"I won't be comfortable supporting a budget until we look internally and make more cuts," 39th Ward Ald. Samantha Nugent said.
The budget impasse was on full display at the City Club on Wednesday featuring two alders against the budget and two for it.
"My fear is if we talk about efficiencies, we are talking about the cuts to services that can possibly be youth employment that can possibly be violence intervention," 26th Ward Ald. Jessie Fuentes said.
The mayor and some of his allies are framing the budget battle as a choice between working people and billionaires.
The Chicago Teachers Union passed out flyers outside of the City Club using that narrative.
"I feel that the ultra-rich should pay more, but it's much ensure that we target that in the right way, that we don't accidentally hit the people we're trying to help," 17th Ward Ald. David Moore said.
Alderman Moore said he is undecided about the mayor's head tax proposal.
He is worried a tax on companies with at least 100 employees can hurt some smaller businesses in his ward.
Moore stood with the mayor as he announced a new Ogden Park Field House in the 17th Ward.
Despite the mayor's help, Moore says a new field house will not influence his vote on budget.
City Council has until the end of the year to pass a budget.