Denouncing Mr. Trump is smart politics in Minneapolis and other big, liberal cities where most people voted against the president and where thousands have marched through the streets to oppose his policies. Some critics say Ms. Hodges — and other Democratic mayors facing troubles with their constituents — have come to see loud opposition to Mr. Trump as a political antidote. What better way to change the subject from local quarrels than to talk about a shared foe?

“She has been given a gift with this,” said Anthony Newby, the executive director of Neighborhoods Organizing for Change, a Minneapolis community group, who criticized Ms. Hodges for what he called a “reluctance to take on the big issues of policing and income inequality.”

But Mayor Hodges’s willingness to call out President Trump is “one shining mark in her administration,” Mr. Newby said. “It’s a great opportunity for her to consolidate what base she has left around an issue that everybody cares deeply about.”