Another round of that perennial question — “Can women have it all?” — was cranking into a full-throttled debate recently, just as Michelle Obama and Ann Romney submitted their entries for a cookie-recipe contest.

It didn’t take long before the critique began, drawing a flurry of online comments reflecting on whether Obama had sacrificed too much by focusing on her children and her husband’s career or had offered a model for working mothers.

Again she was at the center of the open-ended conversation about working mothers that she entered in 2008, when she declared herself mom in chief and made clear her young daughters would be her top priority.

Where the first lady fits into the motherhood debate depends on “how we imagine the arc of her career,” said Anne-Marie Slaughter, the Princeton professor and former top policy adviser in the State Department who kicked off the latest round of chatter in an article in this month’s Atlantic magazine. Slaughter, who left her high-profile policy job after two years to spend more time with her family, said it may be too soon to analyze Obama’s choices.

Perhaps Obama, who has said she expects to always be a working mother of some sort, will return to a full-time professional career after her time in the White House.

“If we imagine that her career will follow the same arc as Hillary Clinton’s, then we can expect her to have a glittering career in her own right once her daughters go to college,” Slaughter said in an e-mail. “And she, like Secretary Clinton, will be in her early 50s when that happens.”

Others have been quicker to form an opinion. The “first mom, gardener thing” is “silly,” said Linda Hirshman, an author, lawyer and feminist. “I do admire the discipline and grit to see that this is the role that you have to play and play it. I could not do it.”

‘Mommy wars’

Obama is not the only well-educated professional woman to be first lady, nor is she the first to come with young children amid the “mommy wars.” Chelsea Clinton was in middle school in 1992 when her father was running for president, and her mother declared on behalf of her generation of liberal women that they had not “stayed home and baked cookies and had teas” but chose instead to fulfill their professions.

Obama, who was an executive at the University of Chicago Medical Center when her husband first ran for president, has taken a different approach, sharing recipes on Pinterest, the online social network. And when Hilary Rosen, a Democratic lobbyist and pundit, said stay-at-home mom Romney had never worked a day in her life, the first lady tweeted, “Every mother works hard, and every woman deserves to be respected.” Rosen apologized.

When Bill Clinton was running for election in 1992 and reelection four years later, Hillary Clinton, who had helped craft a health-care proposal and would eventually run for president, also submitted a cookie recipe for Family Circle magazine’s presidential spouse cookie bake-off.

“Coming so soon in the first-ladies lineup after Hillary Clinton and all of the criticism [she] received for being a nontraditional first lady, anyone holding that role is going to be a little more cautious,” said Katherine Jellison, a professor of women’s history at Ohio University who has studied first ladies.

Obama has effectively broadened the “mom in chief” role beyond her daughters to focus on childhood obesity and helping military families, Jellison said.

Before entering the White House, Obama had an experience more typical of working mothers and wives, and her husband wrote of the arguments they had about sharing household duties.

During his failed congressional run, when he leaned down to kiss his wife goodbye in the morning, all Barack Obama would get is a peck on the cheek, he wrote in “The Audacity of Hope,” describing her anger toward him as “barely contained.”

“ ‘You only think about yourself,’ she would tell me,” he wrote. “ ‘I never thought I’d have to raise a family alone.’ ”

At the time, Michelle Obama was the spouse who put her career on hold to become the children’s primary caregiver. Later, she had help from her mother, Marian Robinson, who would pick up the Obama daughters from school and watch them in the afternoon. Robinson moved to the White House with the first family to continue that role.

Adapting her role

What Michelle Obama has done is adapt “to the needs of her family and career, depending on where she was at any given time,” said Patricia Ireland, a labor lawyer and former president of the National Organization for Women. “When she started at the University of Chicago, she worked many long hours, but when President Obama announced he was going to run for president, she cut her hours 80 percent. Maybe we’re not talking about work and family balance. We’re talking about prioritizing at any given moment.”

Terri Givens, a government professor at the University of Texas and mother of two young sons, said she finds the first lady’s choices instructive. A few years ago, Givens stepped down from her job as a vice provost and went back to teaching, so she could be there for her sons’ after-school activities.

“We’re probably doing the same amount of activity that we were doing when Michelle was a lawyer, when I was vice provost,” Givens said. “We’re not less successful. But in these roles, we have more flexibility.”

Obama’s calendar is first set with her daughters’ school schedules, then her commitments to her husband’s reelection campaign and her own programs. She said she cherishes family dinners.

“I personally . . . know the challenges of leading a busy life at work and at home,” the first lady said in 2009, “trying to do a good job at both — and always feeling like you’re not quite living up to either — and trying not to pit one against the other, really trying to balance it. . . . I call myself a 120 percenter. If I’m not doing any job at 120 percent, I think I’m failing. So if you’re trying to do that at home and at work, you find it very difficult and stressful and frustrating.”