Hello, Operator: Can Bill de Blasio Go From Master Strategist to Mister Mayor?

MR. DE BLASIO, who grew up in Massachusetts, lives in a cheerful but modest yellow South Slope row house with weathered vinyl siding and his Ford Escape hybrid only occasionally parked out front. His daughter Chiara graduated Beacon High School last year and now attends college; his son, Dante, is a high school sophomore at Brooklyn Tech.

“He’s not like a packaged product,” said Mr. Sunshine, a longtime friend of Mr. de Blasio’s. He then paused for a faux-cough that sounded an awful lot like “Mitt Romney,” adding, “He’s very normal, which is maybe the most unique quality of someone who wants to be mayor of New York.”

As evidence of his own normalcy, Mr. de Blasio points to his decision to send his children to New York City public schools. As do his aides, repeatedly. Apparently, kids in public schools amount to a political advantage none of the city’s other recent mayors—nor Ms. Quinn—can claim. “Being a public school parent is a big fucking deal,” Mr. Sunshine explained.

Additionally, besides casting Ms. Quinn as too conservative on economic issues, both Mr. de Blasio and his supporters constantly reference the Quinn-backed 2009 term-limits extension, hoping it will come back to haunt her, four more Bloomberg years later.

While it’s still early in a likely fluid race, according to the public polls, Mr. de Blasio certainly has his work cut out for him. The latest survey gave Ms. Quinn a 65 percent approval rating among Democrats and a solid lead overall, with 32 percent of the total vote. Mr. de Blasio, with 49 percent approval, stood at 9 percent of the total vote. Whether Mr. de Blasio can maneuver his way into anything even close to a lead remains to be seen.

“I think as a political operative he’s had a very long track record of success,” Mr. Wolfson said. “Whether being a political operative is the right background for being a mayor and a chief executive is, in my opinion, a different issue.”

— Additional reporting by Hunter Walker