(Bloomberg) — Whether she wins or loses in the November general election to become New Hampshire’s next governor, Democrat Maggie Hassan will make history.

If Hassan, who won the party’s primary Tuesday, according to the Associated Press, is victorious on Nov. 6, she’ll become only the second woman elected to lead the state. A loss to her Republican challenger, Ovide Lamontagne, would leave Democrats without a female governor for the first time in 17 years.

The Democratic Party has billed itself as the champion of women, accusing Republicans of waging a war on the gender with attempts to restrict access to health care like contraception and abortion. Democrats and women’s groups say the lack of a female state chief executive in their ranks would deprive the nation of a feminine voice to help shape those debates.

“This should be a wake-up call,” said Madeleine Kunin, a Democrat who was elected Vermont’s first female governor in 1984. “You can set the agenda for the state.”

Battles on social issues such as women’s health have erupted at the state level after Republicans captured majorities in 25 legislatures in 2010, boosting their power by the most since 1928. Republicans led the passage of a record 92 abortion restrictions in states last year, more than double the previous high set in 2005, according to the Guttmacher Institute, a New York-based compiler of reproductive-health policy data.

North Carolina’s Bev Perdue and Washington’s Christine Gregoire, both Democrats, aren’t running for re-election. The four remaining female governors are Republicans who won office in the 2010 sweep. Among them were New Mexico’s Susana Martinez, who became the first Hispanic female governor of any state, and Mary Fallin, the first woman to lead Oklahoma.

Lamontagne, who won the Republican primary Tuesday, according to preliminary results from the Associated Press, is a lawyer who has run unsuccessfully for governor before. The 54- year-old Manchester native, who calls himself the “tea party favorite,” opposes abortion except when the woman’s life is in danger and wants to repeal the state’s 2009 same-sex marriage law. Republicans swept into power in New Hampshire in 2010, capturing 75 percent of the more than 400 open seats.

The Democratic Governors Association and Emily’s List, which helps recruit, train and raise funds for Democratic women candidates who back abortion rights, said in a joint statement that a Republican win in New Hampshire would embolden “anti- woman hardliners” to run in more states. Both groups are increasing efforts to recruit and prepare more women to run in 2014, when 36 gubernatorial races will be held after 11 this year.

“The stakes are too high right now to have a country where we don’t have a single female Democratic governor in one of those offices,” Jess McIntosh, a spokeswoman for Washington- based Emily’s List, said in an interview.

Women aren’t monolithic in their political views, and many have led the fights to ban access to abortion and contraception. Still, the gender as a whole tends to vote more Democratic, exit polls show. Obama won the female vote by 13 percentage points against John McCain, his Republican opponent in 2008. New Hampshire Gov. John Lynch, D, who chose not to seek a fifth two-year term, won it in 2010 by 20 points.

The fewer Democrats in power, the better, regardless of gender, said Rae Chornenky, president of the National Federation of Republican Women. The Alexandria, Va.-based group encourages and helps female party members to run.

Democrats are “alleging this mythical Republican war on women,” she said. “Taking aside one social issue gets us off the most important issue: the economy.”

Republicans like Chornenky and Democrats including Kunin say they aren’t content with how long it’s taking political institutions to more closely mirror the demographic breakdown of the populations they represent.

In the election of 1992, dubbed the Year of the Woman, the number of female members of Congress almost doubled to 10 percent. Women now make up 17 percent of the House and Senate, according to the Center for American Women and Politics at Rutgers University in New Brunswick, N.J.

In state legislatures, a pipeline to higher office, gains have been slower. Female representation stands at 24 percent, just three percentage points higher than two decades ago, according to the center.

For statewide elective office - one of clearest paths to governorships, according to McIntosh - it has risen 1 percentage point in that time, to 23 percent, down from a high of 28 percent in 2001.

One reason for the slower growth is that Republican women haven’t made the gains their Democratic counterparts have, said Laurel Elder, who teaches political science at Hartwick College in Oneonta, New York. From 1987 to 2007, the number of women as a share of Republican state legislators declined as Democratic women increased their share 15 percent, according to data she compiled. This year, there are 1,055 female Democratic state lawmakers and 676 Republicans, according to Rutgers.

Of the 93 women currently serving in Congress, Democrats outnumber Republicans more than two to one, according to the Congressional Research Service.

Republicans haven’t made more headway because the “liberal media” doesn’t pay their female candidates enough attention, Chornenky said.

Female representation in New Hampshire’s state legislature has consistently beaten the national average since at least 1975. Hassan, 54, is a former senate majority leader and attorney from Exeter who entered politics as an advocate for people with disabilities, a community that includes one of her two children. She was elected to the state Senate in 2004 and was a member of the 2008 class that made New Hampshire the first state to have a majority-female legislative body.

“We are the last line of defense,” Hassan said in an interview. Jeanne Shaheen, a Democrat, broke the gender barrier in the Granite State’s top office when she won the 1996 gubernatorial election.

The Democrats’ potential predicament of having no female governor is partially self-inflicted. President Obama plucked two fellow Democrats out of office - Janet Napolitano of Arizona and Kathleen Sebelius of Kansas - to join his administration and lead the departments of Homeland Security and Health and Human Services, respectively. Both were replaced by Republicans, Napolitano by a woman.

The appointments were bittersweet victories for advocates of getting more women into office, revealing just how small the pool of qualified women is, said Kunin, a professor-at-large at the University of Vermont in Burlington. In April she published her latest book, “The New Feminist Agenda.”

“When I was elected governor, I thought, ‘Well that’s done,’ “ she said. “I thought I’d look and we’d have a trail of female governors marching behind me. But hardly anyone was there.”