Daniel Lurie, San Francisco’s mayor-elect, beckoned them, one by one, to his four-story brick mansion, perched on a hill, in the city’s exclusive Pacific Heights neighborhood.

The San Francisco supervisors, akin to city councilors, met with Mr. Lurie in his breakfast nook, a half-hour at a time. But despite the luxurious setting — his home has nine bedrooms and is worth $16 million, after all — the conversations, held over the last couple of months, centered on basic, everyday concerns.

They talked about keeping sidewalks clean. Ending illegal drug markets. Filling vacant downtown offices.

And on Wednesday, when Mr. Lurie, a Democrat and heir to the Levi Strauss fortune, is inaugurated as San Francisco’s 46th mayor, he almost certainly won’t mention revolution, resistance or sticking it to President-elect Donald J. Trump, as some liberal mayors tried to do during Mr. Trump’s first term. In fact, the name Trump never appears in the working draft of his speech, an adviser said.

Instead, Mr. Lurie, the founder of an antipoverty nonprofit, will talk about how to turn San Francisco into a well-run city — the best way, he believes, to ensure the future of progressive politics.

“I want to show the world that we can deliver on the promise of our values, that we can be both compassionate and firm,” Mr. Lurie, 47, said in an interview.