Under consideration is a proposal to borrow billions to pay off outstanding debts and plug a $13-billion deficit.
Lawmakers only have a few days to reach a conclusion before the new General Assembly takes over next week.
Also on the agenda is the expansion of gambling across Illinois, including the first casino in Chicago.
The House will begin hearings on the plan before taking a vote. The state Senate approved the plan during the last veto session. Besides allowing the city of Chicago to run a casino, several other communities would get riverboat casinos under the plan, and horse racing tracks would get slot machines.
Supporters believe the plan would generate increase tax revenues.