CHICAGO (Reuters) - The Illinois House will get a second chance to vote on a bill that would give the cash-strapped Chicago Public Schools (CPS) until Aug. 10 to make a $634 million payment to its pension fund, House Speaker Michael Madigan said.

A 53-46 vote in the Democrat-controlled House on Tuesday fell short of the 71 affirmative votes needed to allow the measure to take immediate effect. Madigan told reporters in the state capitol in Springfield that the bill will be called for another House vote on June 30.

"It needs some work on persuading people this is the right thing to do," he said.

The nation's third-largest public school system is struggling to come up with money to make the state-mandated payment by June 30.

Bill proponents said the 40-day delay would give CPS time to get a permanent solution to escalating pension costs that are consuming money needed for educational purposes. House Majority Leader Barbara Flynn Currie, a Chicago Democrat, said the measure grew out of an agreement between Chicago Mayor Rahm Emanuel and Illinois Republican Governor Bruce Rauner.

"With one week until this payment is due, we need our leaders to come together so that we have enough time to reach a solution," said Jesse Ruiz, the school system's interim CEO, in a statement.

Lance Trover, Rauner's spokesman, blamed Madigan for the failed House vote.

"The only reason the speaker's Chicago caucus would vote against the mayor's bill is because Madigan wanted to kill it," Trover said in a statement. Madigan said the statement was "not helpful."

Bukola Bello, a lobbyist for the Chicago Teachers' Pension Fund, told the House Executive Committee earlier on Tuesday the fund's board was neutral on the bill, trusting that the full payment will be made. She added the fund would have to liquidate $100 million in assets to deal with a late CPS payment.

The school system is facing a $1.1 billion deficit in its upcoming fiscal 2016 budget, which has been delayed due to a state budget impasse.

On Wednesday, the Chicago Board of Education will take up a proposal to issue as much as $1.13 billion of tax anticipation warrants and notes for cash-flow needs in the current and next fiscal years.

(Reporting by Karen Pierog; Editing by Phil Berlowitz and Diane Craft)