Mayor Bloomberg didn’t sound very confident today that the city would be able to overturn an arbitrator’s decision blocking the closure of 24 under-performing schools.

“It’s very difficult getting the courts to overturn arbitrators’ decisions,” Bloomberg said from Sun Valley, Idaho, where he is attending the annual Allen & Co. conference of media/technology movers and shakers.

Arbitrator Scott Buccheit stunned the administration last month by ruling the shutdowns would have violated labor contracts.

With just two months to go before all city schools are scheduled to re-open, Chancellor Dennis Walcott announced this week that the 24 would be back in business as usual come September.

The city had intended to replace half the staffs of those schools with new teachers and re-open the buildings under new names.

About 8,000 teachers have applied for what was supposed to be 3,000 openings.

Department of Education officials have yet to say what they’re going to do with those applications.

The mayor described the situation as “difficult.”

“We hired teachers for these spots but they don’t know whether they’re going to have them,” he said.

About 30,000 students are impacted.

“We’re playing with kids’ lives here,” declared Bloomberg. “How the arbitrator could do this I don’t know.”