Michael Madigan is a Chicago Democrat. He says the House will meet Aug. 23 to consider an override. The deadline is Aug. 29.
House Democrats called a vote Wednesday on legislation that incorporates the changes Rauner wants made on a new formula for financing public schools.
Rauner used his veto authority to strip $450 million from Chicago Public Schools. He says his changes provide more money to 98 percent of Illinois districts.
Democrats say districts may get more money initially, but many will lose funding in a few years under Rauner's plan.
Democrats said they wanted to gauge support for Rauner's ideas.
The legislation failed with no "yes" votes, 60 against and 33 members voting "present.'' Republicans complained it was a sham procedure to hide the fact that Democrats don't have enough votes for an override.
Madigan criticized GOP members for not supporting their own governor's proposal.
The Senate voted to override on Sunday.