Chicago Public School finances are “at the breaking point,” Mayor Rahm Emanuel said Monday, arguing the cash-strapped school district cannot afford to make a $634 million teacher pension payment due June 30 — at least not in full.

“If you make that pension payment in its completion, which has been done four years in a row for the first time in a long time … we could no longer make that payment and not have it impact the school building and the classroom,” the mayor said.

“This is the end result of decisions and no decisions made over 20 years. . . . While CPS has made great strides academically, they have postponed the impact of the financial situation from the classroom.”

Never before has the nation’s third-largest school system either missed or reduced a pension payment the district wasn’t authorized to skip by the Illinois General Assembly.

So a partial payment would be a dubious and dangerous first that could trigger a pension fund lawsuit and a further drop in a CPS bond rating already reduced to junk status.

But Emanuel is still holding out hope for a rescue, saying, “Everybody knows in Springfield that, [on] June 30, they, too are on the hook like we are. In the past, you were able to say this was just CPS. But we’ve gotten to the point—it’s a breaking point—that Springfield is on the hook like Chicago . . . not only for the payment. They’re on the hook more importantly for finding a comprehensive final solution that allows us to continue to do what we need to do fiscally, but not do it in a way that endangers the classroom.”

The “breaking point” in CPS finances were outlined in an audit by the accounting firm of Ernst & Young disclosed Sunday by the Chicago Sun-Times.

The audit concluded CPS will “run out of cash as early as this summer” and be unable to meet payroll, pension and debt payments without “third-party intervention.” School could open late, class sizes could skyrocket and sports could be eliminated.

The long-term crisis prompted Ernst & Young to recommend the City Council enact two different property tax increases for the schools totaling $450 million, both necessary even if CPS makes drastic budget cuts and gets the pension relief and increased state funding it seeks from Springfield.

One of the tax hikes would be a “separate levy” of $50 million to bankroll school construction and pay off old projects. CPS has been empowered for more than 20 years to impose the “capital improvement tax” but “never activated” it, sources said. Emanuel is expected to take advantage of it.

The second property tax increase, in the $100 million-to-$400 million range, is far less likely. It’s based on an untested legal theory that, although CPS is hamstrung by a state-imposed property tax cap, the City Council can authorize an even bigger increase and transfer the money to CPS. Legal experts believe it also needs Springfield’s approval.

Asked Monday whether he intends to ask the City Council to approve the increases, the mayor said, “At the right time, we’ll take a look at everything. But we’re not at that point.”

Meanwhile, CPS will ask the Board on Wednesday to approve another $1.1 billion of borrowing against future tax revenue. With no budget proposed for the fiscal year starting July 1, the Board also is expected to allow district officials to spend in the meantime.

The Chicago Teachers Union has accused CPS of going “broke on purpose,” and on Monday, CTU Vice President Jesse Sharkey cited the $50 million potential tax left untouched as another example of that.

“The city also has a responsibility to stop hiding the ball,” Sharkey said. “It turns out there’s a $50 million capital improvement tax they haven’t collected in years?”

“This is all happening behind an appointed board that’s masterminded by (Board President) David Vitale, who’s a banker,” Sharkey said, repeating a call for Vitale’s resignation.

He said before the CTU would join Emanuel in lobbying Springfield for help, the city would have to listen.

“Right now the district wants something from the Chicago Teachers Union: They want our political cooperation,” he said. “But why then is the district refusing to do things that will save them money or [be] cost-neutral that we say will make life better for educators and students? There’s a bit of a disconnect here.”

Ald. Will Burns (4th), newly elected chairman of the City Council’s Education Committee, said he hopes the Ernst & Young report serves as a wake-up call to Republican Gov. Bruce Rauner and Democratic legislative leaders feuding over the state budget.

CPS desperately needs hundreds of millions of dollars in pension relief and a substantial new source of revenue, presumably a state sales tax on services, immediately, the alderman said.

“Nobody’s bluffing,” Burns said. “You have a doomsday scenario where, if no help is coming, this is how dramatic it is.”

Burns predicted Monday that aldermen could be willing to step up. “But that would be contingent of this being part of a deal where the state is kicking in its part, and unions and management are having a realistic conversation about what revenues are available,” Burns said.

Sarah Wetmore, vice president and research director for the Civic Federation, urged CPS to develop a “contingency plan” in case Springfield doesn’t help and then a long-term plan to deal with an “accumulated deficit” Ernst & Young pegged at $5.4 billion by 2020.

“Every year, it’s been one-time solutions to a long-term problem,” she said. “What they need is a long-term plan to get them out of this situation.”

Charles Burbridge, executive director of the Chicago Teachers Pension Fund, reiterated Monday that he expects a full payment because “that’s what the statute requires” for his 63,000 members.

Pressed on whether there are any circumstances under which he would accept a partial payment, Burbridge said, “I don’t know what those circumstances would be. I’ve been in Illinois long enough to know you probably never say never.”