CHICAGO (CBS)– Students will miss a fourth day of classes on Tuesday as the Chicago teachers’ strike continues.

Meanwhile, Mayor Lori Lightfoot said the Chicago Public Schools do not have the money to increase the offers they already made to meet the union’s demands.

“Beyond what we put on the table, there is no more money,” the mayor said Monday afternoon.

Teachers have been on strike since Thursday, and while both sides said there was progress over the weekend, both the mayor and the Chicago Teachers Union have said there is more work to do before they reach a deal.

Negotiations resumed at 9:30 a.m. Monday at Malcolm X College, and Monday afternoon the mayor called on the union to end the strike and send teachers back to work while bargaining continues.

The union balked at the mayor’s request.

“That’s not going to happen,” said teacher and bargaining member Alison Eichhorn. “I don’t know if the mayor’s familiar with what unions do, but we’ve gotten more deals; more tentative agreements in the last two days than we have in 10 months.”

Rallying in Union Park on Monday, other teachers were likewise dismissive of Mayor Lightfoot’s request to end the strike.

“That’s an interesting move,” said teacher Jake Myers. “We could take our one leverage and just throw it away and then she gets all the leverage, so I don’t think we’re going to fall for it.”

“Why would we give in if there’s no promises being kept?” said teacher Barbara Trinh. “It’s not the point of a strike.”

As CBS 2’s Mike Puccinelli reported, the union tried to hold a news conference Monday afternoon. But a man singlehandedly brought it to an end after he started yelling about CTU and CPS through a megaphone and a worker tried and failed to unplug it.

Two major sticking points remain class sizes and increased staffing for nurses, social workers, and other support staff.

Lightfoot said CPS has made a commitment in its contract proposal to provide one nurse and one social worker in each school within five years, and also has written up terms aimed at reducing class sizes, starting with schools with high poverty levels. However, she said the union continues to press for more demands, such as additional pay beyond what the city already has offered, and affordable housing provisions in the contract.

The mayor said the district simply cannot afford to meet all of the union’s demands.

“There are not unlimited resources to fund everything in a single contract that the CTU wishes. The money that we have at the table is all there is,” she said. “With these efforts on the table, we’ve addressed the union’s two core issues that they identified – class size and support staff – and done so in a way that does not compromise the future of CPS or overburden our taxpayers. That was no easy feat.”

The CTU said earlier that they’ve seen movement and made some wins since going on strike. While the union has said they’re encouraged that the city has agreed to put in writing provisions to reduce class sizes and increase staffing, CTU leaders have said the contract also needs enforcement provisions to make sure the city can’t go back on those promises.

“We now have contract language that will protect counselors’ ability to actually counsel our students. We’ve gotten wins for early childhood educators who are looking to protect the particular developmental needs of our youngest students,” said Jennifer Johnson, Chief of Staff for CTU. “We also received a cap on charter school expansion.”

There are still disputes over pay. For example, CPS said their offer will increase average salary to nearly $100,000.

But, CTU says it’s actually nowhere near that.

Meanwhile, the mayor has said missed days will not be made up. If that is the case, and the strike stretches until the end of the week, the average teacher could lose more than $2,000 in pay.

But the union members we caught up with in Union Park said they’re willing to pay a heavy price.

“We lost so much in the last strike that we’re trying to recover some of that, so it’s perfectly all right,” said teacher Ann Bramlett. Sometimes you have to sacrifice to get what you need, and the kids need this.”

The mayor says the union’s demands could end up worsening the city’s already-precarious financial condition.

“Beyond what we put on the table, there is no more money,” Lightfoot said.

She said what is needed now is a greater sense of urgency.

“There needs to be an increased sense of urgency on the part of CTU so we can get the job done, we can reach resolution, we can get our kids back in school,” Lightfoot said.

But union members say the city stonewalled for 10 months. That is why they say the Rev. Jesse Jackson should be brought in as an honest broker.

“Jesse Jackson is a great mediator. We welcome him coming in to be able to get a solution to this,” said teacher Alison Eichhorn. “We want to go back to school.”

“Rev. Jackson is a respected resident of our city and great statesman for our nation. He has won the freedom of American hostages throughout the world and has broken countless labor stalemates throughout the country, and we welcome his participation in these negotiations,” Sharkey added in a statement.

Lighftoot however, said bringing in a mediator at this stage in contract talks would only further delay negotiations.

“When you’ve got a complicated matter like this, and you’re down to the final strokes, hopefully, bringing somebody brand new in that doesn’t have any background or experience in the particulars will only result in delay,” she said.