Jumaane Williams had been onstage for barely 10 minutes when an audience member asked an off-topic question on many New Yorkers’ minds.

“Are you ready to be mayor?” the person said.

The crowd, at a documentary screening in Greenwich Village, cheered in support. The event’s moderators responded enthusiastically. And Mr. Williams smiled. As New York City’s public advocate, he is first in line to succeed Mayor Eric Adams if he were to resign or be removed.

Turmoil surrounding Mr. Adams, capped off most recently by the resignations of four of his top deputies and Gov. Kathy Hochul’s bid to limit his power as he deals with a federal corruption case, has fueled Democratic angst about the mayor’s ability to lead the city. It has also renewed interest in the role Mr. Williams would play in the city’s efforts to chart a path forward.

If Mr. Adams were to leave office before March 26, Mr. Williams would serve as interim mayor for about 80 days before the city holds a special election for a mayor to serve through the end of the term in December. Mr. Williams has not indicated whether he would run for a full term under these provisions. But a growing number of Democrats have called for Mr. Adams to resign or pushed Ms. Hochul to remove him.

Taking over as mayor is clearly something Mr. Williams has thought about. Amid the uncertainty about the mayor’s future, he reached out to three of the departing deputy mayors and asked if they would reconsider leaving if he were to become mayor, according to four people familiar with the matter. At least one of the deputy mayors said they would stay, said two of the people familiar with the matter.