CHICAGO (CBS) — The Chicago Teachers Union on Monday rejected an independent fact finder’s contract recommendation, setting up a possible strike if they cannot reach a deal with the Chicago Public Schools.

“If we don’t make more progress, this is a union that’s prepared to strike,” CTU President Jesse Sharkey said Monday morning.

In rejecting the terms laid out by the fact finder, the teachers’ union moved one step closer to a strike. The union now may vote to authorize a strike at any time, but is legally required to wait 30 days to walk out once they vote.

If a strike did go ahead, it would be the first since 2012.

As CBS 2’s Jim Williams reported, the recommendation that the union rejected involved an offer to boost pay checks – specifically a 16 percent pay increase over five years. Teachers are asking for more than money.

The fact finder’s also calls for a 1 percent increase in health care contributions. The raises recommended by the fact finder would cost approximately $351 million, according to the mayor’s office.

Mayor Lori Lightfoot said the fact finder’s recommendation amounts to a good deal – higher than her proposed 14 percent salary hike over five years.

“That’s real money on the table, folks,” Lightfoot said.

Chicago Public Schools CEO Dr. Janice Jackson said, including raises teachers receive based on experience, the average teacher would see his or her salary rise by 24 percent under the terms recommended by the fact finder. For a second-year teacher, now making about $53,000, their salary would increase to about $72,000 over the life of the deal.

A veteran teacher making $79,000 today would in five years make $98,000 a year.

“This is the largest and most robust salary and benefit package in CTU history,” the mayor said.

For a little perspective, the minimum starting salary for a teacher in the Chicago Public Schools is $52,958. For a teacher in Naperville it is $46,824, and for a teacher in Schaumburg it is $42,320.

But the Chicago Teachers Union says the hang-up is bigger than money.

“Bargaining has gotten more serious lately, which is a good sign, but we’re still a really, really, really long way from having what we need,” Sharkey said.

They want smaller class sizes, and more special education teachers, social workers, and librarians. Four or five years ago, CPS had 400 librarians, and next school year the district will have only 108, according to Sharkey.

“Until that happens, the CTU is going to continue to reject the fact finder report and continue and insist that we see real improvements,” Sharkey said.

Lightfoot said CPS already has taken steps to hire 200 more social workers and 250 more full-time nurses, and agrees the district needs to hire more librarians.

“All of the things they said we wanted which we agree with – more social workers, more librarians, more nurses,” Lightfoot said.

The union is demanding that agreement in the contract. The mayor says it’s in the CPS budget.

“The Chicago Public School budget promises to put less money in our classroom than they spent last year,” Sharkey said. “This is not acceptable.”

“There’s no reason there should be a strike,” Lightfoot said. “We have 30 days to get the job done. We could get this done today.”

The last Chicago teachers strike was in 2012. It lasted seven days and marred Mayor Rahm Emanuel’s first term.

The union warns the threat this year, under Mayor Lightfoot, is real.

The teachers can vote to authorize a strike right now, but would have to wait 30 days before actually walking off the job.

Sharkey said a strike authorization vote likely wouldn’t happen until after the school year starts, so a strike wouldn’t be able to happen until October.

Both sides were back at the bargaining table late Monday.