In 2005, Cohen was arrested for allegedly holding a knife to his ex-girlfriend's throat. The charge was dropped.
Saturday, Daley laughingly chided reporters for not disclosing Cohen's past before Tuesday's primary.
"So, why is it you, now all of a sudden, you're so concerned about it? You all knew about it," Daley said. "It changes now."
The mayor said he would be accused of being a boss or dictator if he tried to pressure a nominee chosen by voters to quit.
