“Quite a few people have approached me with respect to working for greater workplace,” she mentioned, whilst she repeatedly insisted that her focus was on her present job.

However requested to characterize these conversations, Ms. James didn’t draw back.

“That I ought to think about it due to my management, due to my capacity to talk reality to energy, due to my expertise and due to my capacity to unite the state,” she mentioned. “I’m nonetheless centered on the workplace of legal professional common, however I thank them for his or her feedback.”

Her feedback got here after she spoke briefly at a gathering of the Brooklyn Democratic Celebration at Junior’s, a restaurant identified for cheesecake and political occasions.

The scene there supplied one of the vivid illustrations but of how the Democratic major has begun to take form up to now week, with the nascent contours of a marketing campaign path coming into view.

Ms. Hochul, the state’s first feminine governor, was there as properly, a part of her breakneck public schedule as she additionally strikes aggressively to attempt to cement a huge fund-raising advantage upfront of the first. She spoke earlier than each Ms. James and Jumaane D. Williams, New York Metropolis’s public advocate, who introduced this week that he had fashioned an exploratory committee and was contemplating his personal run. (“Nice job as public advocate!” Ms. Hochul cracked wryly.)

Ms. Hochul, Ms. James and Mr. Williams made the rounds via a room filled with celebration activists and elected leaders who clamored for selfies and hugs in between bites of scrambled eggs and sips from precariously balanced espresso cups. Mayor Invoice de Blasio, who can also be regarded as weighing a run, additionally dropped by, a day after he and the others have been at a gathering of Bronx Democrats.

It’s potential that Ms. James could not finally problem Ms. Hochul. She doesn’t have a historical past as a powerful fund-raiser, although her allies are hopeful that because the potential first Black feminine governor in America, she would appeal to nationwide consideration and help ought to she run. She would even have to surrender her present job to run for governor, and she or he would possibly want to hunt one other time period as legal professional common as a substitute — boosted, maybe, by the eye her latest exercise has attracted