Jill Paxton would appear to be the Republicans’ dream. A young suburban mother, Ms. Paxton grew up in a Republican household, has voted against President Obama in both presidential elections, and would like to see the Republicans take back the Senate – a very real possibility on Nov. 4.

She’s perfectly positioned to help make it happen. She’s an Iowa voter, and a Republican win here could tip control of the Senate to the GOP. All Paxton has to do is vote for the woman running for Senate, Republican Joni Ernst.

But she might not do it.

The fact is, Paxton doesn’t agree with Ms. Ernst on several issues that really matter to her, including education and reproductive rights. She calls Ernst “old-fashioned.”

For Democrats facing an energized Republican base and an election map that heavily favors Republicans, voters like Paxton represent a potential lifeline. Republicans need to win six Senate seats to take control of the chamber; two appear in the bag, and of 10 to 12 others that polls show are still in play, eight are in red states that went for Republican Mitt Romney in the last presidential election.

But Paxton offers the hope that, if Democrats can motivate women to vote, they might be able to stop Republicans short of their Senate goal. Indeed, the biggest thing standing in the way of Ernst becoming the first woman to represent Iowa in Congress might be Iowa’s women voters, who strongly favor her Democratic opponent, US Rep. Bruce Braley, according to polls.

Given a generic ballot, the country’s Democrats enjoy a 10-point advantage among likely women voters, while Republicans enjoy a nine-point gap among men, according to a September poll by the Pew Research Center.

In presidential years, this slight difference can work to Democrats’ advantage, because more women than men vote. In midterm years like this one, the number of women voters drops – and Democrats have to scramble to get them to the polls.

There are other pitfalls for Democrats, such as a big drop in the approval rating of Mr. Obama among women – only 44 percent compared with 55 percent in 2012, according to a Washington Post/ABC News survey. But in tossup states, such as Iowa, North Carolina, Georgia, Kentucky, and Arkansas, Democrats are counting on women voters to make the difference.

“Democrats believe that if they can turn out enough women they can overcome whatever advantages Republicans have because of the political environment,” says Jennifer Duffy of the independent Cook Political Report.

At first blush, Ernst seems to have all these advantages, with enthusiastic Republican support, bushels of charisma, and a compelling biography.

She’s an Iowa farm girl who “walked beans” as a kid, and is serving in the Iowa state Senate. As a lieutenant colonel in the Iowa Army National Guard, she ran convoys from Kuwait into southern Iraq in 2003 – boots-on-the-ground experience.

With the same energy as the Harley she rides and the gun she shoots, Ernst burst from a crowded Republican field in the June primary with a memorable TV ad titled “Squeal.” In it, she says she grew up castrating hogs on a farm. She’ll cut pork in Washington, too. “Let’s make ’em squeal,” she smiles from a hog barn.

But she has not played the woman card. Her messaging toward women is “subtle,” says Kathie Obradovich, political columnist for The Des Moines Register.

Not once during three campaign stops on a recent day does Ernst tout herself as potentially Iowa’s first woman senator. Her energetic and sharply focused campaign message is boilerplate GOP: Her opponent is a Washington insider, part of the problem; she’s a fighter for Iowa values who will lower taxes, reduce rules and regulations (including repealing “Obamacare”), get tough on national security, and retire Sen. Harry Reid (D) of Nevada from his leadership of the Senate – always her biggest applause line.

Nothing she says is really directed at women voters explicitly, except perhaps her shorthand descriptor: “Mother. Soldier. Independent leader.”

“I talk to people regardless of gender, whatever the issue is,” she says in a brief interview as she heads to her campaign bus. “We focus on overarching issues and how to make lives better, not through governmental regulation, not through governmental control of every aspect of our life, but the broader issues that are out there.”

Ernst is taking the safe route, speaking to her base – male voters, says Dianne Bystrom, director of the Carrie Chapman Catt Center for Women and Politics at Iowa State University in Ames. She has been polling well with men – though a Des Moines Register poll from Oct. 3-8 shows that advantage has slipped, from a whopping 22-point edge among men in the newspaper’s previous poll to a 15-point one now. That’s even with Representative Braley’s advantage among women.

When asked at campaign stops why they like Ernst so much, men generally cite her decisiveness and directness, her military background and leadership. And then there’s this summary: “She’s cute. She’s got a uniform. She shoots. She rides motorcycles. What’s not to like?” says Ed Wright, a libertarian farmer running for Congress in Iowa’s Third Congressional District.

Paxton could offer an answer.

One Iowa woman’s view of Ernst

Over a hamburger and fries on a break from her financial services job, Paxton explains why she’s leaning toward Braley, originally thought to be a shoo-in to replace retiring Sen. Tom Harkin – the folksy, liberal Democrat who has represented Iowa in both houses of Congress for 40 years.

She starts with what she doesn’t like about Ernst – telling in a race saturated by negative ads. As a state senator, Ernst voted to defund Planned Parenthood. She wants to abolish the US Department of Education, though she would keep federal help for college loans. She opposes the federal minimum wage.

Education is a major concern for this mother of a 5-year-old and 7-month-old, who lives in West Des Moines with her boyfriend, the children’s father. “Braley’s wife is a teacher, and his mom teaches. That makes me believe he’s not going to do anything to hurt education,” she says.

Braley, who has represented Iowa’s First Congressional District for the past eight years, might not have Ernst’s flair: He’s a former trial lawyer who has stumbled from a series of campaign missteps and gaffes about farmers and Iowa’s senior senator, Republican Chuck Grassley.

But he’s doggedly pushing issues that appeal to unmarried women, in particular, bringing up equal pay, college affordability, women’s health and reproductive issues, and the minimum wage (more women than men earn the minimum wage).

He promises never to privatize Social Security or raise the retirement age. He wants to increase the federal minimum wage to $10.10 an hour. And he vociferously warns about Ernst’s cosponsoring of a “personhood” amendment to the Iowa Constitution. If the amendment were ever adopted, it would mean life legally begins at the time of conception. Braley claims it would end all abortions, even in cases of rape or incest; disallow in vitro fertilization; and restrict some forms of birth control.

The race, according to the RealClearPolitics poll average, is in a statistical tie, with Ernst up by just over one percentage point.

For her part, Paxton is torn. She voted for Republican presidential candidates Mitt Romney in 2012 and John McCain in 2008. She could support a candidate like Ernst, who sticks up for farmers, small-town Iowa, and Republican values. On the other hand, “some of her views, like [defunding] Planned Parenthood, that’s really old-fashioned,” Paxton says, picking up a French fry. “That view is like, 1970!”

Such comments are daggers to Republican strategists, who are trying to improve the party’s standing with women, young people, and minorities.

In August, Politico reported on a study commissioned by two major Republican groups, including Crossroads GPS, the nonprofit started by Karl Rove.

The internal study, based on eight focus groups and a poll of 800 registered female voters over the summer, found that women view the GOP as “intolerant” and “stuck in the past.”

Republicans “fail to speak to women in the different circumstances in which they live,” for instance, as breadwinners, Politico quoted from the study. The report’s solutions? Neutralize Democratic attacks that the GOP doesn’t support “fairness” for women, deal honestly about differences over abortion and then move on to other subjects, and pursue innovative policies that “inspire women voters to give the GOP a ‘fresh look.’ ”

Some Republicans are trying to do that. Over the summer, Terri Lynn Land, who is trailing Democrat Gary Peters in Michigan’s US Senate race, responded to criticism that she opposes pay-equity legislation and legal abortion, including in cases of rape. She put up this buzzed-about ad:

“Congressman Gary Peters and his buddies want you to believe I’m waging a war on women,” she says. “Really?” Pause. “Think about that for a moment.” Then she takes a sip of coffee to give viewers time to do just that, finishing up with, “as a woman, I might know a little bit more about women than Gary Peters.”

It’s unclear whether the ad worked. The RealClearPolitics poll average has Peters up by nine points.

Other Republicans have released ads that show them standing up for women victims of domestic violence. And on the campaign trail, some mention support for over-the-counter birth control.

GOP strategists and leaders in Congress “are talking about the Republican Party needing to change their messaging toward women,” but not much has happened, says Professor Bystrom.

“There’s nothing to indicate that the messaging really has changed very much from 2012,” she says. That’s when Democrats seized on some offensive remarks by Republican Senate candidates and claimed that the GOP was waging a “war on women.” It cost the GOP two Senate seats.

Dialing back the ‘extreme’ image

Ernst is often called the Sarah Palin of Iowa (she was endorsed by Ms. Palin), and Braley constantly points to her “extreme” tea party agenda. But Ernst has softened her message since she handily won her primary.

In their Sept. 28 televised debate, Ernst dialed it back, calling the personhood amendment “simply a statement that I support life.” She also said, in response to a question about her discussing privatizing Social Security, that she has “not endorsed one option over another.”

Instead of running ads in which she is riding a Harley in her black leather jacket, Ernst is running ads this fall showing her in a home setting or driving around the state and meeting with men and women voters. She’s talking about protecting Social Security for her mom and dad; wanting good schools, jobs, and affordable health care; and “bringing people together.”

So what does this mean for the outcome of this race?

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For Braley to pull this one out, Bystrom says, he’ll have to bring out his base and convert some independent women, and even some moderate Republican women.

Women like Jill Paxton.