Michelle Obama comes to the 2012 Democratic National Convention with a delicate task: helping her husband’s campaign reach out to women, who are a vital part of his coalition, without veering too far into an increasingly polarized battle over women’s issues.

The first lady, who is scheduled to speak Tuesday night, has been circumspect about what liberals call the Republican “war on women.” She did not participate in the Obama campaign’s “Romney/Ryan: Wrong for Women” tour last week, which condemned the Republican ticket’s positions on abortion. When she appeared on David Letterman’s show Wednesday as a bit of counterprogramming to the GOP convention, she responded to a question about Rep. Todd Akin (R) — the Senate candidate in Missouri who said that women who are raped are unlikely to get pregnant — by allowing that “dumb guys” say “dumb things.” But that was it.

As she prepares for the convention, Obama is one of the most popular political figures in the country, viewed favorably by nearly seven in 10 Americans. That means she can sell her husband, who is considerably less popular, rather than having to sell herself, as she did four years ago, when she was the less liked of the two. But she must be careful to advocate for him without appearing too partisan.

The 2008 convention “was very much about introducing her and in many ways the president to the country through an unfiltered lens,” said Stephanie Cutter, deputy manager of the Obama campaign. “This convention is more about just reminding people about the values and vision that drive the president every day and some of the decisions that have been made over the last four years that have moved us forward.”

But refreshing the public’s memory of the man behind the presidency is a more challenging task than the one Obama faced last time, when she acknowledged Barack Obama’s “funny name” while vouching for his values. In her convention speech Tuesday night, advisers said, she will try to speak to her husband’s disaffected supporters, giving them, as she says on the campaign trail, “the chance to see up close and personal what being president looks like . . . the problems with no easy solutions, the judgment calls where the stakes are so high and there is no margin for error.”

She will have to find new anecdotes that give insight into the president’s character to reach those people — particularly women, said Jennifer Lawless, director of American University’s Women and Politics Institute. “The fact that she is pretty honest about him and calls attention to some of his flaws and makes him seem like a real person is appealing,” Lawless said.

At the same time, she will be tasked with bringing attention to Barack Obama the family man, trotting out onstage with perfectly styled first daughters Sasha, 11, and Malia, 14.

In the campaign speech the first lady gives as she rallies supporters across the country, she talks about the “brilliant” women sitting on the Supreme Court because of her husband, about his administration’s support for equal pay for women in the workplace, and about how “Barack Obama believes women should be able to make our own choices about our health care.”

At a moment when women’s reproductive health has unexpectedly become one of the highest-profile issues of the campaign, and when women’s votes are expected to be critical to deciding the tight race, Michelle Obama will have to step gingerly, discussing the issue without seeming overly partisan.

The tougher talk about abortion rights has come from the president, who said recently that “we shouldn’t have a bunch of politicians, a majority of whom are men, making health-care decisions on behalf of women.”

Michelle Obama’s appeal to voters has been shaped more by television interviews, magazine covers and her best-selling gardening book, “American Grown.” During the 2008 campaign, her favorability ratings took a hit when she said that “for the first time” in her adult life, she was proud of her country. Conservatives repeatedly brought up the statement and called her unpatriotic. But since moving into the White House and adopting her role as mom in chief, her popularity has soared.

“The good news is her likability factor is high, so she doesn’t have to sell herself as a likable, good person. She can sell the idea of ‘why you need to reelect my husband,’ ” said Elizabeth Mehren, a professor of journalism at Boston University who has written extensively about first ladies. “This is her moment to step forward and talk about the fundamental concerns that working women have with the economy.”

Obama has not directly tackled such concerns. Instead, she recently acted as “guest editor” of iVillage, a Web site that caters to women. In an extensive interview there, the first lady kicked off her shoes and curled her bare feet up on the couch in her East Wing office. She gave tips for healthy eating, discussed the ways she talks to her daughters about body image and talked about how her husband quit smoking.

“His ability to ultimately kick the habit was because of the girls, because they’re at the age now where you can’t hide,” Obama told iVillage. “I think that he didn’t want to look his girls in the eye and tell them that they shouldn’t do something that he was still doing.”

Michelle Obama is less well-liked by Republicans. Only 38 percent of them give her a favorable rating, and conservative commentators have accused her of advocating a “nanny state” in her push for healthier school lunches.

But the approach has made Obama a public figure in her own right, with “a popularity that transcends partisanship to a certain degree,” said Carl Sferrazza Anthony, a historian who studies first ladies and presidential families.

“What she brings to her [convention] speech is not just her role as the wife of the candidate, the partisan, the spokesman, but also almost a certain rational objectivity [and] this larger-than-life charismatic public personality,” Anthony said. “She has a real credibility, and she comes to that podium with those factors intact. Whether the campaign will seek to maximize that, we’ll have to see.”

Obama’s appeal seems aimed squarely at women — mothers in particular — who will be key decision-makers in this election. The Romney campaign acknowledged the importance of moms last week as well, with Ann Romney using her remarks at the Republican National Convention to talk about love and give a shout-out to “the moms of this nation — single, married, widowed — who really hold this country together.”

On Wednesday, while Republicans were making their case in Tampa, the first lady used part of her time on Letterman’s show to talk about parenting. The interview kicked off with Obama and Letterman chatting about summer sleep-away camp and healthier school-lunch standards. Pizza “is going to be served on a whole-wheat crust” with strips of green peppers or carrots on the side, she said.

She stuck to the approach that Obama campaign aides have called “relentlessly positive.” In response to Letterman’s question about whether the close race is stressing out her husband, she said: “Barack is so — the levelheadedness that you see is real. He doesn’t bring that energy home.”

Camille Johnston, the first lady’s former communications director, said the convention speech will show Obama’s fun-loving personality while making the case for her husband’s administration. “The speech that she will give will be something that she has crafted in her own voice and with her own attention to detail and with her own style,” Johnston said. “She prepares diligently for important moments.”

On Letterman’s show, the first lady said her convention speech will be serious, adding that she will not be cracking any jokes.

“I’m still taking it in,” she said of her prepared remarks. “So over the next couple of days, I’ll just get the words and understand. . . .

“You know, it’s feeling what I’m saying,” Obama said, closing her eyes, “not just learning the words.”