By Colleen Leahey
May 14, 2013

FORTUNE — Christine Quinn has been called brash, controlling, volatile, hotheaded, aggressive, and more. Is New York City’s candidate for mayor comfortable with those descriptions? “Pretty much,” she shrugged. “I’m tough, and New Yorkers deserve that.”

At Monday night’s Fortune Most Powerful Women dinner in Manhattan’s Time Warner Center, New York City Council Speaker Quinn was interviewed by Fortune senior editor -at-large Pattie Sellers in front of an audience that included HSN (HSNI) CEO Mindy Grossman, Goldman Sachs (GS) executive Dina Powell, and Barbara Bush — as well as the 27 global leaders participating in the final week of the Fortune/U.S. State Department Global Women’s Mentoring Partnership.

Quinn honored Fortune’s 2013 MPW Summit theme, “Breakthroughs in Leadership,” by discussing her run for mayor and the ceilings she will shatter, should she win: Quinn, 46, will be not only the first female mayor of New York City, but also the first one to be openly gay. She is leading in the latest polls by a wide margin.

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The New York City Council Speaker position is equivalent to Congress’ Speaker — but in a way more powerful, says Quinn, because there’s only one House. She works closely with current Mayor Michael Bloomberg, who founded and ran Bloomberg for twenty years before leaving Wall Street for politics, though the connections their careers created greatly differ.

Noting that much of the success Bloomberg has had as New York City mayor stems from his ability to mobilize his network of wealthy and powerful people, Sellers asked Quinn about her lack of that kind of currency. “Look, the mayor knows a bunch of people,” she responded. “[But] the main thing Mike Bloomberg did was he picked up the phone and asked business leaders to take a break from their business lives and come to government.” She added, “I’ve never picked up the phone and had business leaders say no. That’s never happened.”

Quinn believes these executives were happy to help Bloomberg because they know that if New York City does well, then their business will also do better. “The message to take from Mike Bloomberg isn’t, ‘If you’re not as rich as so-and-so, forget about it.’

The lesson is: Pick up the phone, ask for help, and people will want to say yes. “Typically, even if they’re not a billionaire, people call the Mayor of New York City back, you know what I mean?”

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Beyond her politics, Quinn’s straightforward demeanor has won over some and pushed away others; her personal strength is both an advantage and a detriment. But, as noted earlier, she couldn’t care less. Quinn cites her mother as the source of this confidence.

“My mother was abundantly clear with my sister and I. We were to figure out what we wanted to be, and then we were to be exceptionally good at it.” The idea that success was out of reach because of gender or some other hurdle was not a thought floating about Quinn’s childhood home in Glen Cove, N.Y.

Much like Bloomberg, Quinn has few qualms about asking others for help. A perfect example: In 2011, when budgets cuts threatened to force layoffs of 4,000 public school teachers, she called the head of the Municipal Labor Committee, Harry Nespoli. He asked what she wanted him to do.

“I said I’m not 100% sure, but if you don’t like the concessions the mayor’s put out, then give me other ones.” Nespoli brought together a group of experts, and they came up with $80 million in concessions, which altered the conversations, and they were able to reduce the layoffs.

“The best thing to know is what you don’t know,” Quinn said. “Don’t bullshit it if you don’t know it. Just get somebody who does, and you can usually then get to a solution.”

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