The teacher pension crisis that threatens to end the Chicago Public School year three weeks early caused yet another major break Tuesday in the once-close friendship between Mayor Rahm Emanuel and Gov. Bruce Rauner.

Emanuel branded Rauner the “emperor who wears no clothes.” A spokesperson for the 6-foot-3-inch governor fired back that the 5 foot-8-inch mayor of Chicago sounds like someone who has a “Napoleon complex.”

Emanuel and Rauner were once close friends, fellow school-reform advocates, travel companions and business associates who made millions together.

The latest crack in their relationship occurred after a difficult three-day period for the governor that saw Chance the Rapper denounce Rauner after a face-to-face meeting on the teacher pension crisis and write a $1 million check to CPS that will barely make a dent in the financial crisis that threatens to shorten the longer school year that Emanuel took a teachers strike to secure.

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“In the last 48 hours, everybody has come to the conclusion that the emperor wears no clothes. The governor. There’s nobody else [he can blame]. He can’t blame Mike Madigan. He can’t blame John Cullerton and the Grand Bargain. He can’t blame me. He can’t blame Chance. And . . . everybody’s now seen what he stands for,” the mayor said after a ribbon-cutting ceremony at a new riverfront office building.

“We’ve gone three years without a governor who has introduced a [balanced] budget. Governor’s State [University] now is cutting 22 academic programs,” Emanuel said. “Kids from the state of Illinois are leaving the state to go to college when we used to be a net gain. Ounce of Prevention and other social service agencies are suing the state. More people are leaving our state . . . and this is all under his tenure.”

The governor’s office issued a cutting, one-line rebuttal to the latest mayoral broadside: “Sounds like someone has a Napoleon complex,” said the governor’s spokesperson, Eleni Demertzis.

Emanuel scoffed at the school funding plan the governor hastily put together hours before Chance wrote a $1 million check to the Chicago Public Schools Foundation.

It calls for the mayor to use $215 million in tax-increment financing funds to fill the gap caused by the governor’s veto of a bill that would have given CPS that same amount in pension help already built into the school budget.

The mayor has already hit Chicago homeowners and businesses with a $250 million property tax increase for teacher pensions — and $588 million more for police and fire pensions and school construction. And Emanuel has already used an $87.5 million TIF surplus to stave off another teachers strike.

“Strong public schools are a bedrock of a city. Our taxpayers already paid for everybody else’s teachers pension. I am not gonna recommend a third tax to cover up for the failure of the state of Illinois,” Emanuel said.

The mayor urged Rauner to do three things.

“One, introduce for the first time in his tenure as governor, a balanced budget. Two, don’t undermine the Grand Bargain that you said you were for, but then called people up to your office and tell them to vote no. Three, after your [school funding] commission, finally introduce legislation on a school formula that doesn’t punish kids for being minority or poor, but actually helps them get ahead and break the cycle of poverty,” the mayor said.

“I think I can say this, at least for the city of Chicago and the taxpayers and the students and the teachers: We’re exhausted and exasperated from the rudderlessness under Rauner,” Emanuel later added.

In the Machiavellian world of Chicago politics, some have assumed that Chance inserted himself into the high-stakes fight over school funding to benefit Emanuel. After all, the rapper’s father, Ken Bennett, is a former deputy chief of staff and director of the Office of Public Engagement under the mayor.

But the mayor insisted Tuesday that he “did not talk to” Chance.

“The assumption or accusation or insinuation is condescending to Chance. He’s a product of Chicago. A nationally and internationally acclaimed artist. He went to Chicago Public Schools. He credits the Chicago Public Libraries for his ability to start putting music together,” the mayor said.