WASHINGTON – Hillary Clinton has a not-so-secret weapon working for her as she seeks the presidency: women.

Just 12 days into her campaign, the New York senator and former first lady has made it clear that appealing to female voters will be central to her message, and not the afterthought it has been in past presidential campaigns. Already, her campaign says, young women in particular are drawn to her candidacy and the prospect of electing America’s first woman president. Officials with the Clinton campaign cite anecdotal evidence from supporters and from the turnout of women at early campaign events.

Single women, now 51 percent of the female adult population, also represent a key demographic to the Clinton campaign. Her campaign plans appeals aimed directly at their concerns– including healthcare, retirement, and education– to boost turnout among a demographic that has been less likely to vote than other groups.

Overall, “54 percent of the electorate in 2004 were women; I think potentially that could go up in 2008,” says Ann Lewis, a senior adviser to the Clinton campaign.

Already, polls show higher percentages of women supporting Senator Clinton than the male candidates in both the race for the Democratic nomination and in general election matchups. But history has shown that women’s votes alone, long key to Democrats’ electoral chances, cannot win elections for Democrats. So the question is whether, in running a campaign highly attuned to women, Clinton can avoid alienating men.

“She has to balance it out,” says Debbie Walsh, director of the Center for American Women and Politics at Rutgers University.

Part of the balancing act involves efforts by her campaign to warm up her image, which some voters find cold and calculating. The setting for the Jan. 20 Web video announcement of her exploratory committee was a living room, not an office. She calls her campaign a “conversation,” she has “chats,” she “listens.” She used the same approach in her 2000 Senate campaign, successfully, but the challenge now is to carry that out on a national scale– with an electorate that has seen her in action for 15 years and feels it already knows her.

Jon Stewart on “The Daily Show” served up a string of jokes this week around Clinton’s campaign slogan, “Let the Conversation Begin.” “Look, this might not be the most politically correct thing to say, but I don’t think that slogan’s gonna help you with men,” he began, to big studio-audience laughter.

Another part of the calculus for Clinton is that she is running to become commander in chief during wartime. So not only does she face stereotypes about women and military matters, but she also faces her party’s generation-old image as being weak on defense. During her time in the Senate, she has cultivated an expertise on defense and foreign policy, and taken high-profile trips to Iraq and Afghanistan. But, if she wins the nomination, it remains an open question whether she can overcome those hurdles.

Though it is early in the nomination race, she looks to be in good shape against the other Democrats.

In a Gallup poll released Wednesday, among Democratic and Democratic-leaning voters, 47 percent said she would do the best job on Iraq, compared with 26 percent for Sen. Barack Obama of Illinois and 19 percent for former Sen. John Edwards of North Carolina. On terrorism, she won with 49 percent. But on domestic issues, she had more support: 57 percent on the economy, 67 percent on healthcare, and 63 percent on education.

One of the great unknowns for Clinton, if she wins the nomination, is what percentage of voters really is willing to vote for a qualified woman for president. Recent polls show the number in the 80s. But when asked if they believe their neighbors would be willing to vote for a qualified woman as president, the number drops into the low 60s.

“I think someplace between 86 and 61 percent may be where the reality is,” says Ms. Walsh, referring to polling data from last year. “I also think it’s very hard now to ask this question generically. You’re getting two things at the same time– you’ve got the theoretical question, and then you’ve got Hillary in there, so it’s no longer abstract. It’s a real person with a real record.”

Another element of attitudes about Clinton is that portion of the population that viscerally dislikes her. Many are people who would never vote for a Democrat anyway, but this phenomenon could affect her ability to win independent voters– a segment of the electorate essential to any winning campaign. Some analysts question whether Clinton’s gender will really inspire an outpouring of women to support her.

“I don’t think Hillary can count on women coming out for her out of a sense of sisterhood,” says Carrie Lukas of the Independent Women’s Forum. “She’ll have to earn women’s votes just as other Democratic candidates have really tried to court women.”