Those chasing Ms. James believe that the numbers have surely changed since then because of the high percentage of undecided voters. Ms. James’s closeness with the governor, whom she marched with in the West Indian American Day Parade, has, at times, been viewed as a liability, as her opponents have suggested that she was least capable of being independent of Mr. Cuomo.

Ms. James said she has sued both Mr. Cuomo and Mayor Bill de Blasio and remains independent.

“There will be no sunlight between me and the law,” Ms. James said.

During the debate, it was clear her opponents believed that Ms. James may have facilitated a shift in momentum by saying to The New York Times that she did not want to be known as the “Sheriff of Wall Street,” and suggesting at last week’s debate that not everyone in Albany was corrupt.

Ms. Eve made clear her intent to attack Ms. Teachout from the very beginning, declaring in her opening statement that when she spoke about being an independent voice for vulnerable New Yorkers, it was “not rhetoric, and certainly not a classroom exercise” — a barb that elicited an audible ooh from the crowd.

Mr. Maloney stopped short of calling Ms. Teachout a liar, but just barely, calling her attacks and rebuttals “just false” or a “pile of nonsense.”

“This is like the tale of two Zephyrs,” he said, adding, “I have seen the good Zephyr. This is not it. This is the attack Zephyr that wants to win a political campaign.”

The debate was co-moderated by Preet Bharara, the former United States attorney in Manhattan who was fired by President Trump; there had been speculation that Mr. Bharara was interested in running for the seat, which is being filled by Barbara D. Underwood.