Advocates expect the Senate to take up the matter on the floor Tuesday.
House Minority Leader Tom Cross and Senate Minority Leader Christine Radogno announced Tuesday that they'll back the proposal.
The plan awaiting a Senate floor vote would allow the 250,000 illegal immigrants who are already driving the chance to be tested, licensed and buy insurance.
Cross and Radogno were no-shows two weeks ago when Senate President John Cullerton announced the plan.
Cross said he hadn't seen the legislation but supports it now. Radogno says both parties have worked on it for five years.
