The measure is designed to lower costs and change union work rules at the lakeside convention center.
A half dozen of the largest shows have threatened to leave Chicago because of the high cost of doing business here.
"I can't imagine the governor not signing it. If for some reason he got confused and vetoed the bill, we would quickly go back to Springfield and override his veto and make it the law of the land," said Sen. John Cullerton, Illinois Senate president.
Trade show managers that met with top lawmakers Thursday said they would be willing to keep their shows in Chicago if this overhaul measure is approved and does indeed lower costs.