Mayor Rahm Emanuel said Wednesday he is prepared to do “some very difficult things” to keep the Chicago Public Schools afloat and argued that the nearly bankrupt school system is $596 million in the hole only because state government is Illinois’ “largest deadbeat.”

“I understand that the governor wants to blame [Comptroller] Susana Mendoza, wants to blame the speaker, wants to blame the Senate president, wants to blame me, wants to blame the Supreme Court. I would like him to do his job just like the Chicago Sun-Times editorial said,” Emanuel said.

“Your primary responsibility is to pass a budget and work with other people. It’s not everybody else’s fault when you haven’t done the primary job that you got elected to do and he has not done that and we’re now all paying the price for it. We’ll meet our obligations. We’ll step up and do ’em. We will do some very difficult things. But it cannot absolve the state of their responsibility and they are A.W.O.L.”

Earlier this week, Emanuel’s Chief Financial Officer Carole Brown came clean with the magnitude of the problem needed to meet the mayor’s demand to stave off a threatened early closing of Chicago Public Schools.

Brown disclosed that CPS needs $596 million — five times more money than the $129 million gap previously made public — because of a delay in receiving block grants from the state.

Brown also said that absolutely everything is on the table to solve the problem. She even refused to rule out another tax increase — in addition to the $250 million already imposed for teacher pensions and the $45 million for school construction.

But, Brown pointedly noted that would not solve the need for an immediate cash infusion.

Rauner spokeswoman Eleni Demertzis was quick to respond to the mayor’s latest broadside.

“CPS’ crisis is not due to the budget impasse, it’s due to decades of fiscal mismanagement,” she wrote in an email. “Instead of pointing fingers and blaming decades of fiscal mismanagement on a governor who has been in office for two years, CPS officials and the mayor should be here in Springfield demanding that the comptroller prioritize our schools and urging lawmakers to pass a balanced budget that includes pension reform that will in return secure the $215 million in funding for CPS.”

The Rauner administration has blamed the comptroller for the $457 million in state block grants built into the CPS budget, but not yet forwarded to district.

“Any outstanding payments from the state lie with Comptroller Mendoza, and can be processed when her office chooses,” Demertzis has said.

Mendoza spokesman Abdon Pallasch has argued that, absent a state budget, the comptroller lacks the cash to make more payments. “Like the check bouncer who yells at his bank for bouncing a check from an account he himself emptied, the governor disingenuously blames the comptroller for not writing checks from state coffers that Gov. Rauner emptied,” he said.

Emanuel was asked why he waited so long to reveal the magnitude of the problem to aldermen whose support he needs for a CPS rescue that could put the city’s own shaky finances at risk.

“The bills kept climbing and growing and, in every aspect, they said they were gonna get current with it. … The state of Illinois is the largest deadbeat in the state of Illinois,” the mayor said.

After canceling two closed-door briefings with aldermen, Emanuel shed no new light on the rescue plan. He would only reiterate Brown’s statement that “everything is on the table” and that, even another tax increase or reinstating the employee head tax he proudly eliminated has not been ruled out.

Other possibilities include: a bridge loan from tax-increment-financing (TIF) districts that may never be repaid; another round of borrowing; more cuts of school support staff; delayed payment to CPS vendors, and a request to the Chicago Teachers Pension fund to delay a $721 million payment due on June 30.

A 60-day delay would solve some of the cash-flow issues, since tax revenue typically rolls in by August.

Ald. Howard Brookins (21st) was incensed by the $596 million shortfall and the hide-the-ball strategy at CPS and the mayor’s office.

“I don’t know why they think solving a problem everybody knows they have in the dark is gonna make it better,” Brookins said Wednesday. “My committee and aldermen have no authority over CPS. But they’re gonna look to our committee to solve the problem and it’s a much bigger problem than we thought.”

CPS is in a bind for a second straight year after balancing its budget by counting on state money that had strings attached or didn’t come in on time because of Springfield’s budget standoff.