CHICAGO (Reuters) - Illinois Governor Bruce Rauner expressed optimism on Monday that the financially struggling state could begin fiscal year 2017 on Friday with a temporary budget in place.

The nation's fifth-largest state has limped through the current fiscal year without a complete budget, relying on court-ordered spending and ongoing and stopgap appropriations to operate in the wake of an impasse between the Republican governor and Democrats who control the legislature.

Lawmakers ended their spring session on May 31 without passing a new budget, raising questions over Illinois' ability to operate for a second straight fiscal year without a spending plan.

Rauner is pushing legislation to fund crucial Illinois services until January and K-12 public schools for the entire fiscal year.

"I think the good news is it looks like we pretty well have an agreement on the stopgap budget itself," Rauner told reporters at a state capitol news conference, characterizing remaining differences with Democrats on spending levels as minor.

The governor warned the school funding bill remains imperiled by Democratic demands for a Chicago Public Schools (CPS) "bailout" that he refuses to support.

"CPS has been financially mismanaged for decades. It's not the fault of the people of Illinois," Rauner said, adding that bankruptcy was a better option for the district.

The third-largest U.S. public school system had been seeking $480 million from Illinois for teacher pensions and a revamping of the state school funding formula to ensure more money flows to poor students.

Senate President John Cullerton is hopeful that a bipartisan budget plan and school funding bill will come up for votes when the legislature meets on Wednesday, according to a statement from his office. Steve Brown, a spokesman for House Speaker Michael Madigan, said the House will "vote on measures that reflect the progress that has been made by the stopgap budget working group."

The governor also brought up a proposal by Chicago Mayor Rahm Emanuel to allow city funds to be invested in debt issued by other Chicago governmental agencies, including "junk"-rated CPS. Rauner said the move, introduced in the city council last week, acknowledges Chicago's responsibility for the district, which is controlled by the mayor. But he said the city's purchase of CPS debt would amount to "kicking the can down the road."

An Emanuel spokeswoman said the proposed ordinance was sought by the city treasurer and has nothing to do with the fiscal crisis at CPS.

(Reporting by Karen Pierog; Editing by Matthew Lewis)