Brady, who was the Republican nominee for governor, accepted a lunch invitation from Democratic nominee Quinn, who won a close race.
They got together for corned beef sandwiches and potato pancakes at Manny's South Loop deli.
They exchanged compliments and agreed to try to cooperate on issues such as infrastructure improvements and high-speed rail, and reforming pensions, Medicaid, and workmen's compensation.
"All these things are really not Republican issues or Democratic issues," Quinn said. "They are Illinois job issues. So I really hope we can forge some common ground there, next week and in the weeks to come."
"We agreed that budgetary reforms need to take place," said Brady. "I don't believe the appetite in the legislature is there for a tax increase. If not, I think he realizes that spending has to be reduced."
One area of agreement was that Quinn paid for both lunches.
Brady will buy when the governor visits him in his hometown of Bloomington.
