By Monica Davey Steven Yaccino

CHICAGO — When it comes to demanding, pushing and sparring, few people could even begin to compare with Rahm Emanuel, the famously foul-mouthed mayor whose no-holds-barred tactics once included sending a dead fish to someone whose work he found lacking.

Then came Karen Lewis.

In Ms. Lewis, the president of the Chicago Teachers Union, which on Tuesday completed a second day on strike from public schools across this city, Mr. Emanuel may have met his match.

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