Gov. Bruce Rauner on Tuesday issued an amendatory veto on a long-awaited education funding bill that he’s dubbed a “bailout” for Chicago Public Schools.

In his veto message, Rauner said the bill “places the burden of the Chicago Public Schools’ broken teacher pension system on our rural and suburban school districts.”

“This is not about taking resources away from Chicago,” Rauner wrote. “This is about making historic changes to help poor children in Chicago and throughout the state of Illinois.”

Rauner on Monday vowed “swift action” when the Illinois Senate sent over the bill but decided to sit on it overnight. Senate Democrats met the Monday deadline the Republican governor had been demanding for a bill that would rewrite how state money is allocated for poor students and send pension money to the Chicago Public Schools.

Rauner for weeks said he wanted to take out the Chicago teachers’ pension money and divide that amount among other school districts.

According to the governor’s office, the veto removed a minimum funding requirement; the Chicago block grant from the formula; the normal cost of pick-up for CPS pensions and unfunded liability deductions. It also removed “escalators” that he believed would increase costs, among other changes.

With just weeks before schools are scheduled to open for the fall, House Democrats accused Rauner of playing politics. And the governor accused them of the same.

Mayor Rahm Emanuel, meanwhile, accused the governor of “ignoring the needs of Illinois’ school children, the desires of school superintendents across the state, the voices of newspaper editorials across the state, and the recommendations of his own education funding commission.”

City Hall was still analyzing precisely how much money the governor’s veto would cost the broke Chicago Public Schools.

“His math is fuzzy. His claims have been proven false. And the only thing the governor’s action advances is his own personal brand of cynical politics,” the mayor was quoted as saying in an emailed statement.

“It is well past time for Governor Rauner to stop playing politics with our children’s futures, start demonstrating leadership, and ensure a child’s education isn’t determined by their zip code or his political whims.”

To override the governor’s veto, Emanuel needs to round up 36 votes in the Senate and 71 votes in the Illinois House.

That’s not a challenge in the Senate, where there are 37 Democrats and where the school funding formula passed the first time with 35 votes.

The House is a different story. There, the original bill passed with just 60 votes on a day when a handful of Democrats were missing.

Still, a top mayoral aide gave the override a good chance of passing both houses. That’s, in part, because Rauner eliminated a permanent hold-harmless provision and substituted a two-year guarantee that school districts would not receive less state aid than they current get.

“He’s keeping it for two years, then it goes away. That helps our cause because the bottom falls out in two years. That will have a drastic impact on school districts, especially Downstate,” the Emanuel adviser said.

“Every day that goes by, the chances of an override improve because there is no alternative. At the end of the day, there will be enough legislators who do not want to see schools fail to open. I believe we will be able to work with them to accomplish the override.”

The mayoral aide was asked whether Emanuel was prepared to raise taxes again to fill any gap created by Rauner’s veto.

“The mayor has made a commitment that our schools will open [on time] and stay open. That will not change,” the Emanuel aide said.

As the clock ticked Monday, state lawmakers were trying to negotiate changes to the bipartisan education spending plan in the hopes of settling the latest disagreement between the Democrat-controlled Legislature and the Republican governor before classes are set to resume within weeks.

Democratic leaders have said an amendatory veto is dangerous because there are several ways in which the measure can fail. With an amendatory veto, the Senate must either vote to accept the changes, which is highly unlikely, or vote to override. The measure would also be dead if the Senate didn’t take up the veto. Should the Senate fail to override, the measure will die. That would mean there would be nothing in place to get state aid to schools to open in time this fall. Legislators would have to go back to the drawing board and craft a new measure.

If the measure is overridden in the Senate, it must still be overridden in the House, where Madigan would have to round up House Republican votes as he did in passing a tax and budget package.

Procedurally, a vote to accept the changes would need a supermajority of votes. An override would need the same support. Rauner on Tuesday seemed to dispute that, saying it will take a simple majority to accept his veto changes. When told that an Illinois Supreme Court decision — and Illinois Senate Democrats — said otherwise, Rauner said lawmakers could choose to create a new bill that could be passed with a simple majority. That, too, procedurally would need a 3/5 majority since it would be made effective immediately and because votes would be cast after May 31 — the end of the regular spring session.

Democratic leaders last week said too many changes in the governor’s amendatory veto might mean it won’t pass constitutional muster. Rauner laughed off that suggestion last week. But the amendatory veto will be carefully reviewed by an Illinois Senate parliamentarian either way.