Democrats face a tough electoral environment this fall. President Obama’s approval ratings are among the lowest of his tenure and analysts say Republicans have a good chance to take control of the U.S. Senate.

But in one area, at least, there is plenty of room for growth. Only one female Democrat holds a governor’s office: New Hampshire’s Maggie Hassan.

Advocates are determined to add to the total. And their best opportunity, it appears, is in New England.

Hassan is favored to win re-election. Massachusetts Attorney General Martha Coakley has a sizable lead in the early Bay State gubernatorial polls. And Rhode Island Treasurer Gina Raimondo is running neck-and-neck for the Democratic nomination in her state.

“When you think about the grouping here of New Hampshire, Massachusetts and Rhode Island, we’ve really seen a change — a momentum of women stepping up and running,” said Stephanie Schriock, president of Washington-based Emily’s List, which raises money for Democratic women candidates nationwide.

Hassan, Coakley and Raimondo account for half of the gubernatorial candidates Emily’s List is backing nationwide. And they look, at the moment, like the group’s top prospects.

Another Emily’s List gubernatorial candidate, Mary Burke of Wisconsin, is in a relatively tight contest. But Wendy Davis of Texas and Allyson Schwartz of Pennsylvania face steeper odds.

The paucity of female governors is an embarrassment for a Democratic Party that puts a premium on diversity — and relies on women voters on election day.

And while New England can claim the only female Democratic governor at the moment, this liberal corner of the country does not have a particularly strong record of electing women to the corner office.

Only New Hampshire, Connecticut, where Ella Grasso served in the late-1970s, and Vermont, where Madeleine Kunin served in the late-1980s, have elected female Democratic governors.

In recent years, the party’s most prominent women governors have hailed from the Midwest and West — Jennifer Granholm of Michigan, Kathleen Sebelius of Kansas and Janet Napolitano of Arizona.

“New England has lagged a little bit,” said Kate Coyne-McCoy, a Rhode Island-based political consultant who launched a super PAC focused on electing Raimondo. “But we’re catching up. Women are raising lots of money and are building competitive campaigns across the region.”

The New England candidates are running on a whole range of issues — from trimming health care costs to building economic equality. But gender is playing a significant role in their campaigns.

Last weekend, Coakley stopped by a Fitchburg diner with the city’s mayor, Lisa Wong, at her side. And when she visited a pair of elderly women seated in the corner, she dropped a favorite line.

“When I graduated from law school,” she said, “my dad gave me a plaque that said ‘sometimes the best man for the job is a woman.’ ”

In an interview with WBUR — near a prized, 19-pound zucchini the diner’s owner had pulled from his garden and hung on the wall — Coakley said it’s more important that Massachusetts elect a Democrat than a woman. But she argued that an inclusive state is a stronger one.

“Women and others that have not been involved in the political system actually enrich it,” she said.

But the growing number of female candidates — if welcomed by advocates — has created some awkward moments.

Homeland security expert Juliette Kayyem, a Democrat, was the first woman in the Massachusetts gubernatorial race. And she got some initial support from Emily’s List.

But when the better-known Coakley got in the five-way Democratic primary, Emily’s List backed her — and suggested that Kayyem drop out.

Kayyem said any effort to clear the way for a single woman candidate is misguided.

“The strategy of one woman at a time has not worked well for State House runs for Democratic women,” she said. “We have one female Democratic governor [nationwide]…. So why not try a different approach?”

Emily’s List says it approaches races on a case-by-case basis, doing whatever makes the most strategic sense. Sometimes it stays out of a primary with multiple female candidates, sometimes it gets in.

The group encourages its national network of 3 million donors to donate to endorsed candidates. To date, according to Emily’s List spokeswoman Marcy Stech, donors have given “six figures” to the three New England gubernatorial candidates.

That there is so much focus on the region is not a surprise, said Marni Allen, director of Political Parity, a nonpartisan project aimed at electing more women to high office.

Allen’s research suggests that Democratic-leaning states are more likely to elect women to high office. It has also identified a multiplier effect. “Once a state elects one woman to high-level office,” Allen said, “a second woman is more likely to succeed in that state.”

Massachusetts elected its first female U.S. senator, Elizabeth Warren, two years ago. New Hampshire has an all-female congressional delegation and a woman in the governor’s office.

The glass ceiling has proven more durable in Rhode Island. But Raimondo, the treasurer, is the state’s strongest female candidate for high office in recent memory.

Her campaign is not rooted in gender; the former venture capitalist — locked in a tight race with Providence Mayor Angel Taveras and lawyer Clay Pell for the Democratic gubernatorial nomination — actually fares a bit better among men than among women in the polls.

But she is best known for pushing pension reform through a strong union state. And she is pitching herself as a politician who can work collaboratively to get things done.

“You know, people have said to me that women are better at getting everybody together, overlooking the politics, just focusing on a solution,” she said, at a recent “Women Helping Women” fundraiser for a women’s homeless shelter. “I certainly know that’s my skill.”

Advocates hope her good-government pitch will play particularly well in a state dealing with the latest in a long-run of government scandals; last month, then-Speaker of the House Gordon Fox resigned in the face of a criminal investigation.

But the high-powered figures at the “Women Helping Women” fundraiser, many of them supporting Raimondo for governor, suggested their support is rooted in a broader appreciation for her record and values. And in a bit of gender solidarity.

“I’m not voting for her just because she’s a woman, although I am biased,” said bank vice president Stephanie Preston, laughing. “We are phenomenal.”

Coyne-McCoy, the Rhode Island-based political consultant, hopes to turn support for Raimondo into donations to her American LeadHERship political action committee.

Coyne-McCoy, who worked for Emily’s List for a decade, is holding off on major fundraising while the gubernatorial candidates consider a “People’s Pledge” that would discourage outside spending.

But she says she is prepared to spend on advertising, get-out-the-vote operations or whatever makes the most strategic sense. And she is ready to be “bruising.”

Emily’s List, in addition to tapping its fundraising network for direct donations to candidates, has a political action committee that can make independent expenditures.

In 2012, the group spent $700,000 to mobilize 51,000 independent women voters in New Hampshire — the bulk of it focused on the governor’s race and the balance on a pair of U.S. House races.

Correction: An earlier version of this report omitted Connecticut’s Ella Grasso from the list of female Democratic governors in New England. We regret the error.