Illinois lawmakers are considering a major overhaul of the program that provides medical care to the poor, part of an effort to control costs during a budget crisis and build support for a tax increase.

The legislation would emphasize HMO-style “managed care” and reduce the use of costly institutions for people with physical and mental disabilities. It would require the state to pay Medicaid bills sooner, reducing late-payment penalties. It also would take steps to ensure ineligible people don’t sign up for medical care.

The lawmakers who negotiated the changes predict they’ll save at least $800 million over the next five years. That would amount to roughly 2 percent in a program that costs about $7.6 billion a year.

But with the state budget in a shambles, legislators are searching desperately for any place to save money. In addition, Democratic leaders trying to pass an income tax increase could point to the Medicaid changes as evidence that they’re cutting back and not simply grabbing for taxpayers’ wallets.

Gov. Pat Quinn met repeatedly with legislative leaders Wednesday, searching for some version of a tax increase that could attract enough support to pass. There were no indications of a breakthrough that might generate the mix of Republican and Democratic votes that would almost certainly be needed to pass such a touchy measure.

Quinn, Senate President John Cullerton and House Speaker Michael Madigan want to pass something before the current General Assembly formally ends Jan. 12. After that, they lose some of their Democratic majority and the outgoing “lame-duck” legislators who might be persuaded to support a tax increase as they leave office.

The state’s budget deficit could hit $15 billion this year.

The Medicaid legislation passed in the Illinois Senate 58-0 and now goes to the Illinois House.

Sen. Heather Steans, D-Chicago, acknowledged the changes would save relatively little money. But she and others portrayed it as an important first step toward streamlining Medicaid.

“This is turning an enormous ship. It’s hard and it’s going to take a lot of work,” Steans said.

The bill would require at least half of Medicaid clients to be placed in HMO-style managed care by 2015. It also would make it easier to transfer money to help move disabled people from expensive institutions into cheaper residential care.

Another change would end a policy that allows Medicaid bills to go unpaid for months. That practice costs the state late-payment penalties and disguises the depths of Illinois’ financial problems.

Other changes would help ensure that only eligible people enroll in Medicaid. Clients would have to provide additional evidence that they meet income requirements, live in Illinois and, for continuing clients, that they’re still eligible.