Maybe they can run against Jane Byrne:

The two candidates face a challenge when it comes to the issue. They’re tackling corruption because it looms large after numerous scandals under Daley’s watch. But they also don’t want to anger the mayor by criticizing him on the topic.

I’m not denying that it’s a sticky wicket: trying to figure out how to run against the Daley that’s unpopular in the polls while running with the Daley that probably would win if he ran for reelection.