Ms. Taylor is vehement on the subject.

“The thing I actually find really interesting,” she said in an interview, “is that the only things Michael’s opponents have come up with to disparage him with are things that happened a long time ago, and were part of the culture then, and are nothing to do with anything he’s done.”

“You need to look at people’s values and what they have done,” she continued. “A couple of words that somebody said to somebody many years ago is not who they are today. You regret it, you apologize, you make it right, you move on and you live your life according to the values of what you have.”

In a way, it is odd that Ms. Taylor should find herself in the spotlight solely for the purpose of supporting a man’s ambitions.

She has spent a lifetime navigating a world of men, always succeeding on her own. At Dartmouth, she was in the second class of women to graduate, one of just 200 women among 3,000 men. (When she brought Mr. Bloomberg to her 40th reunion, she said, she got an award for “best trophy date.”)

She made her own way at Columbia, working nights and weekends at two different jobs, after her father refused to pay the tuition on the grounds that she would just marry anyway, and then went on to Wall Street, where she worked at companies including Smith Barney and Lehman Brothers.

In 2010, the Republican Party recruited her to run for the United States Senate in New York, but she turned down the offer. (She has also since switched to the Democratic Party.) Even though her relationship with Mr. Bloomberg, who was mayor at the time, meant the public knew her mostly as New York City’s unofficial first lady, Ms. Taylor said, she did not feel relegated to second place.

“I’ve never thought about it,” she said at the end of many hours of campaigning, from San Francisco to Walnut Creek and in between.