CHICAGO (CBS) — Despite rejecting a four-year contract recommended by an independent fact-finder, the Chicago Teachers Union might not be going on strike before the end of the school year.

The Chicago Teachers Union has expressed concerns about a potential strike’s impact on teachers’ health insurance and paychecks if a walkout were to continue into the summer break.

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The soonest teachers could go on strike would be May 16, with little more than a month left in the school year.

CTU Vice President Jesse Sharkey told the Chicago Sun-Times, unless Chicago Public Schools leadership follows through on a threat to revoke a longstanding 7 percent pension benefit, he doesn’t believe teachers will be going on strike in May.

Sharkey noted many teachers are paid over 10 months, rather than having their salaries spread out over the entire year, and don’t want to give up their last paychecks of the school year. He also said there are questions about whether teachers would risk losing their health insurance if they go on strike in May.

On Monday, Mayor Rahm Emanuel praised the CTU leadership for their decision not to strike now.

“What I would say is, in the remaining weeks to the school year, our teachers will continue to focus on the education of our children and to the leadership, I would say join us in convincing Springfield to properly fund education in the state of Illinois,” Emanuel said.

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Monday afternoon the union issued a statement saying, “The Union’s members have yet to decide when or if we will strike in the coming days or during the next school year.”

A fall strike offers much more financial security to teachers, according to labor professor Bob Bruno. He says if they strike now they risk losing this month’s pay and health care for the entire summer. Strike after school starts, they resume health care after they return and could recoup lost wages.

“Even if there were some loss days of pay, there is a high likelihood, just like in 2012, at the end of the school year you’re going to tack those days on and you’re probably not going to lose any pay,” Bruno said.

The CTU committee tasked with setting a strike date was scheduled to meet Wednesday.

According to the Sun-Times, the union also is concerned about keeping the support of parents who already have been forced to scramble to make plans for their kids on furlough days and a one-day teachers strike last month.

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Teachers also are loath to go on strike with final exams coming up. CPS has said it would have to cancel final exams if teachers walk off the job in May.