As concerns have grown about violent crime, she released a policing and public safety plan that includes hiring a civilian police commissioner and creating a new commission to decide whether to fire officers accused of misconduct. She was early in urging Mr. de Blasio to fire his police commissioner, Dermot F. Shea, after his aggressive response to last year’s protests.
Yet she has also distanced herself from the defund slogan, saying the term “means different things to different people.” In contrast, Ms. Morales has embraced the movement and pledged to slash the $6 billion police budget in half — a stance that has endeared her to left-leaning voters, less so to more moderate ones.
At the same time, some business and civic leaders fear that Ms. Wiley is too liberal; in a poll of business leaders, Ms. Wiley was near last place with just 3 percent. They also question whether Ms. Wiley has enough experience as a manager to run a sprawling bureaucracy with a $98 billion budget.
“Maya is terrific, but business is looking for a manager, not an advocate,” said Kathryn Wylde, the leader of a prominent business group.
At the moment, Ms. Wiley is simply looking to connect to as many voters as she can, in person and on social media, where she posts campaign diaries recorded at home.
She lives in Ditmas Park, Brooklyn, with her partner, Harlan Mandel, in an elegant house built in the Prairie School architectural style made famous by Frank Lloyd Wright. They have two daughters, Naja, 20, and Kai, 17. Ms. Wiley is Christian and Mr. Mandel is Jewish, and they belong to Kolot Chayeinu, a reform congregation in Park Slope.
The last woman who came close to being mayor, Christine Quinn, a former City Council speaker, said she regretted that she tried to soften her hard-charging personality during her campaign. Her advice for Ms. Wiley was to be herself.