By Francesca Trianni

NEW YORK (Reuters) – At Cubbyhole, a popular New York lesbian bar, for every two revelers who praised City Council speaker, Christine Quinn, in her race to become the city’s first woman and first openly gay mayor, one complained about her style and political policies.

“Just because she’s a lesbian, it doesn’t mean I’ll vote for her,” said Veronica Gonzales, 32, who works for a non-profit organization. “She is not socially liberal enough, and she has this air about her like she is above it all – like she is above us.”

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While fellow candidate Anthony Weiner’s extramarital sexual transgressions have dominated the headlines, a perplexing reality of the race for mayor of the nation’s largest city is Quinn’s failure to lock up the votes of women and gays, even though she herself is both.

Quinn is the only woman in the race, and the only openly gay candidate, yet she scored only 30 percent support from women in a survey by Quinnipiac University published on July 29. Polls do not break down voting preferences by sexual orientation.

The presumed front-runner of the six candidates vying to succeed Michael Bloomberg has failed to crack the 40 percent level of overall support, the percentage needed to win the Democratic primary on September 10 and avoid a runoff between the top two finishers.

In a runoff with black candidate William Thompson, Quinn would lose 50 percent to 40 percent, the Quinnipiac poll found.

Despite its progressive reputation, New York City has elected few women to citywide office. The best known was Elizabeth Holtzman, who held the top financial post of comptroller from 1990 to 1993. The most recent was Betsy Gotbaum, public advocate until 2009, although Quinn as speaker of the city council is considered the most powerful official after the mayor.

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VOTERS AMBIVALENT

In New York’s Greenwich Village, with its significant gay and lesbian population, support for Quinn was mixed.

Gonzales plans to vote for Public Advocate Bill de Blasio, who she said is “more straightforward about his agenda.”

The ambivalence has contributed to a sense that Quinn is unable to close out the race, and one of the other candidates could overtake her, even as support wanes for Weiner.

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“Right now, all signs point to a runoff, and with voters not connecting with anyone in particular, it’s going to be a fluid race,” said Lee Miringoff of the Marist poll. “It is very important for Quinn to sharpen her message so that she starts to get into a better shape to do better down the road.”

Voters critical of Quinn most often mention her style, which some view as brash and calculating. Quinn’s backing of a temporary change in the city’s term-limits law, which allowed Bloomberg and other lawmakers to run for a third term, has also been used against her.

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De Blasio has positioned himself as a liberal alternative to Quinn on issues such as funding for universal pre-kindergarten programs and preventing hospital closings.

“She needs to do better in the long run with women voters,” Miringoff said. “If she is going to be successful she needs to create a greater appeal among women voters. And to do that, she needs to put her campaign in an historical context.”

In recent weeks, Quinn, long an outspoken proponent of gay marriage, has sought to portray her candidacy as an historic opportunity for New York women.

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This week, the Quinn campaign rolled out endorsements from the National Organization of Women and feminist political activist Gloria Steinem.

At the annual Gay Pride parade in Greenwich Village, Quinn marched alongside Edie Windsor, the New Yorker whose U.S. Supreme Court case paved the way for gay couples to receive federal benefits this year, leading more than 1,000 backers.

Quinn’s campaign said it planned targeted advertisements on Facebook asking women to “Make history with Chris Quinn,” and targeting women voters through house parties and phone banks.

Mike Morey, Quinn’s spokesman, noted that she had fought to save education jobs, keep firehouses open and expand access to pre-kindergarten during difficult fiscal times.

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“She will continue making the case through Election Day that she is the only candidate who has a real record of results delivering for the middle class,” Morey said.

Back at the Cubbyhole, as a performer clad in black leather shorts and a red wig danced in the background, Jaimie Ho, 35, a structural engineer, said she was not sold on Quinn.

Ho remembered seeing Quinn at the pride parade: “She didn’t seem accessible. She had a ton of body guards around her.”

“I like her background. I like the work she has done in the City Council,” continued Ho. “But I ask myself: Is it fair to vote for her simply because she is gay? There needs to be more substance.”

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(Reporting by Francesca Trianni; Editing by Greg McCune and Gunna Dickson)