The embattled alderman's corruption case put one of the front runners, Susana Mendoza, on the defensive yet again.
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Mendoza, who once called her Burke her political mentor, once again tried to distance herself from him Wednesday.
"Whatever actions Chairman Burke may or may not have done, those are reflections on his actions and his ethics, not on mine," Mendoza said.
During the Chicago Tribune Editorial Board forum, Mendoza likened her Burke connections to convicted former Governor Rod Blagojevich.
"As a state legislator I led the impeachment efforts against a governor that some point I believed in, and as it turned out he was a bad guy," she said.
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Other candidates talked of reforms that the Burke corruption case has made into an issue in the mayor's race, including term limits.
"For every municipal office. Same thing with a smaller City Council. We do not need 50 alderman, we have to get rid of aldermanic privilege," said Bob Fioretti, candidate for mayor.
"I supported term limits when Pat Quinn pushed it for all elected officials," said Paul Vallas, candidate for mayor. "I support barring secondary incomes from being earned. I support, I support rotating of these committee chairs."
Political newcomer John Kozlar suggested a fresh face might be the best reform.
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"Chicago can, in the next four years, elect one of four individuals that will elect the same machine style politics, or they can elect somebody new and fresh like myself, who's not tied to the past," he said.
Dorothy Brown found herself in the hot seat over her own unresolved federal investigation into alleged job selling in the County Clerk's Office.
"I made the decision to run for mayor because I refuse to let the individuals that went over there and falsely accused me to stop me, after I've even properly prepared to do this job, I refuse to roll over and play dead for them," Brown said.
Burke's case had been set for a preliminary hearing Friday, in which additional details of the case could have been revealed. But federal prosecutors have asked a judge to push the case back until May to allow 90 days for a grand jury to hear the case.