Chicago has grown accustomed to being a political punching bag. For years, Republicans have used the city’s real problems with crime and corruption as a sort of dystopian shorthand for all that ails Democratic cities.

Mayor Brandon Johnson has cast himself as a counterpoint to that caricature.

In speech after speech, he refers to Chicago as the “greatest freakin’ city in the world.” He once said, “If you don’t live in Chicago, you don’t have a right to talk about the city of Chicago.” And as some expressed trepidation about hosting this week’s Democratic National Convention, Mr. Johnson, 48 and in his first term as mayor, insisted that Chicago was ready, arguing that “there’s nowhere else in this country that could handle the gravity of what we’re experiencing right now.”

Municipal pep talks aside, Mr. Johnson’s first 15 months in City Hall have not been easy. Chicago has struggled to take in tens of thousands of migrants, many of them bused in by Texas conservatives making a political point. Voters rejected a plan the mayor campaigned on to raise tax revenues to address homelessness. And a contentious City Council debate about whether to call for a cease-fire in Gaza exposed divides on the political left, with Mr. Johnson casting the tiebreaking vote in favor of the resolution.

As the Democratic Party comes to town this week — along with journalists, law enforcement officials and thousands of left-wing protesters furious with the Biden administration — Mr. Johnson, who is expected to speak from the main stage on Monday night, believes that this convention has the potential to reframe the conversation about Chicago.

But if things go poorly, it could also reinforce the old, unflattering impressions of a big city run by Democrats. For the mayor, just like for his city, it is a week loaded with opportunity and risk.