There's a crisis brewing in a major city's public school system

Chicago Public Schools are having a tough time right now.

The US government is investigating Chicago Public Schools (CPS) for possible financial misconduct.

Meanwhile, the city's school system faces a huge budget gap, and the governor of Illinois even suggested bankruptcy might be the best option for the district.

"This investigation is very sad, I hope there's been no wrong-doing, but Chicago Public Schools has been a source of patronage, cronyism, dealings, massive bureaucracy," Illinois Gov. Bruce Rauner said to CBS Chicago on Monday.

"It hasn't really served the families and the parents of the children in a very long time," he added.

A key figure in the federal investigation is CPS CEO Barbara Byrd-Bennett, who's on a paid leave of absence while investigators look into a $20.5 million no-bid contract awarded to a private company called SUPES Academy, the Chicago Tribune has reported.

That award money has come under fire since Byrd-Bennett was once employed by SUPES Academy, a company that trains teachers and administrators, prior to her role at CPS. Byrd-Bennett was hired in 2012 by Chicago Mayor Rahm Emanuel, and in 2013 she signed the request for the board to consider the contract for SUPES Academy, according to records cited by The New York Times.

The federal investigation of possible misconduct further complicates Emanuel's already-controversial strategy of using the private sector to improve public education. It also comes at a time of financial uncertainty for the public school system, which faces a potential shortfall of $1.1 billion next year, according to the Chicago Tribune.

And further challenges lie ahead, as contract talks have begun between the school district and the Chicago Teachers Union. The last meeting between the two groups in 2012 spurred a teachers' strike.