“If I wasn’t here, my children wouldn’t see a representation of themselves,” said Representative Ilhan Omar, Democrat of Minnesota.

Representative Cathy McMorris Rodgers, Republican of Washington, and her husband, a Navy veteran and stay-at-home father, moved their three children to the nation’s capital — a politically charged decision.

Representative Katie Porter, Democrat of California, spends close to 20 hours a week commuting between Washington and Irvine, Calif., where her three children live.

Speaker Nancy Pelosi delayed her entry into electoral politics until most of her five children were adults. She ran for her San Francisco district only when her youngest daughter was preparing to graduate from high school.

Since then, the line separating political ambition and motherhood has all but disappeared. (Of course, men have never had to choose between fatherhood and a political career.) Senator Kirsten Gillibrand is making her children a focal point in her quest for the 2020 Democratic presidential nomination. Representative Liz Cheney’s five kids have hardly impeded her rapid ascent up the Republican leadership chain.

And the demand from voters was clear after a historic wave of women was elected in November: They want political representatives whose families and life experiences reflect their own.

But the trials of mothers with school-age children in Congress are many: long commutes, extended absences, emergency duties, late-night soirees, fundraisers.

While fathers with young children are a mainstay in Congress, there are less than 30 such moms in the House and two in the Senate. Several say they still feel a stigma attached to their decision to hold office before their children are in high school, even if motherhood offers a critical perspective on governance.

“The normal is actually somebody who’s more like me, who’s juggling and piecing it together,” said Representative Katie Porter, a freshman Democrat and single mother who has three children at her home in Irvine, Calif.

And it is reflected in national trends: Two-thirds of Americans believe men and women should be equal at both work and home. But a recent survey shows that roughly a quarter of people have a more nuanced view: that while women deserve equal opportunity in employment and politics, they should do more of the child rearing and homemaking.

In Congress, the mothers see that reproach when colleagues and strangers ask if the children are O.K., implying that they could somehow be damaged by their mothers’ absences. They feel it in the pressure to still do it all, to be there for votes and for dinner whenever possible. They suffered through it when in the middle of a record-breaking government shutdown, lawmakers made a show of promising to give up their salaries in solidarity with government workers — and the mothers worried about paying their bills.

“Society might want to see your children as a weakness,” said Representative Ilhan Omar, Democrat of Minnesota. But, she added, “they can be your greatest asset.”

“They can be a clear reminder as to why it is urgent for you to do this work,” she said.

Ms. Porter made dinner for her children and their friends. Representative Katie Porter Democrat of California Ms. Porter determined on a recent Wednesday at her home in Irvine that family day for Team Porter would start when she picked up two of her three children at the bus stop. Wednesday is double-coupon day at the grocery store; then comes a Slurpee run at 7/11 and homemade hamburgers for dinner. Ms. Porter making a grocery list with her son Paul and daughter, Betsy. But between those moments, she still needed to plan the rest of the week — two staff members had spread fund-raising documents around the kitchen table — and make a trip to a nearby television studio to weigh in on Deutsche Bank and Democratic oversight. By the front door, a whiteboard calendar tallied how many days she would not be home this month. Ms. Porter during a television appearance near her home in Irvine. Meantime, there is an unexpected visit from two friends, and the eventual clean-up of a Nerf gun battle awaits. Her three children — Luke, Paul and Betsy — describe a whirlwind between the campaign and Ms. Porter’s first months in office: long, sometimes dull campaign events; getting to meet other children in Washington; and, for Betsy, the newfound realization that her mother also has homework. Ms. Porter with her eldest son, Luke. Ms. Porter talking to her staff in Washington. Pausing midconversation, Ms. Porter brushed Luke’s hair aside before pressing on what comes next: “You think we should do one term?” “No, Mom,” said Luke, 13. “You either don’t do it or you do it until you die.” Ms. Porter during a tour of Mission Hospital in Mission Viejo, Calif.

In the Public Eye

One question Ms. Porter gets all of the time is just as telling: How are the children?

She knows her answer — they are doing well. But outside of the polite exchange, Ms. Porter, a former law professor, scoffs at some of the alarm she faces for leaving her children at least four days a week.

She recalled a trip to Burma that she took as a professor, during which she had little cell service for two weeks. “How is this any different?” she asks.

Her male colleagues, she notes, probably do not get the same question.

The public fascination with Congress members and their lives — particularly when they are in their districts — usually manifests itself in smiles, waves and encouragement. (During one grocery trip, a fellow shopper asked a reporter if someone could tell Ms. Porter she was doing a great job.)

But in other instances, the attention has more dangerous consequences.

After President Trump in April used a tweet to tie Ms. Omar, a Muslim, to the Sept. 11, 2001, attacks, the congresswoman became the target of numerous death threats — prompting Ms. Pelosi to ask the Capitol Police to evaluate protections for Ms. Omar and her family.

“My older kids are acutely aware of the uptick in death threats,” Ms. Omar said, “and they’re part of the public discussion about the threats.”

“They know that we have a principle of not cowering to bullies,” she added.

They also know that having a Muslim mom in a public role “will ultimately draw a lot of negative as well as positive attention,” she said.

Representative Ilhan Omar Democrat of Minnesota Ms. Omar has found, more than most of her freshman colleagues, that even in Minneapolis, maintaining a domestic routine can be difficult among the disruptions that come from her newfound celebrity. Ms. Omar spent her first weekend in Minnesota after being sworn in helping her daughter Isra, 16, pick out a dress for a school dance and convening a family dinner at their usual booth in the back of a Perkins Restaurant and Bakery. Ms. Omar and her daughter Isra shopping in New Hope, Minn. Those activities had to be scheduled around a visit to the Minnesota State Capitol to speak with furloughed government workers and reviews of a speech before a women’s march. “If I wasn’t here, my children wouldn’t see a representation of themselves,” Ms. Omar said of her place in Congress. “Not only my children but a lot of children like them can see themselves having a seat at the table someday because we are opening that door for them.” Ms. Omar took a selfie with supporters in Minneapolis at the Women’s March, where she also spoke. As one of the highest profile members of the new class of Democratic representatives, she is constantly swarmed by supporters clamoring for a photograph or offering a word of encouragement — and she is also constantly attacked by vitriolic critics. Ms. Omar said after a conversation about the realities of being a member, it was ultimately her family’s decision to remain in Minnesota in order to prevent disrupting both school and her connection to the district. “Time is the biggest challenge, but we find creative ways to connect with FaceTime and text messages throughout the day,” she said over email. Ms. Omar with constituents and her staff at the Minnesota State Capitol. Ms. Omar and her husband, Ahmed Hirsi, having dinner with their daughters Isra and Ilwad and son, Adnan. Ms. Omar’s remarks about Israel — some of which she has apologized for — and the outrage not only from Republicans but also from many Democrats have led to an alarming uptick in death threats. “But when they know I’m O.K.,” Ms. Omar said of her three children, “they’re O.K.”

Leading by Example

Practically every mother in Congress has a person, most often a woman, she has peppered with questions before a campaign or turned to for confidence midsession.

Ms. Porter points to Senator Elizabeth Warren of Massachusetts, who is running for president and also is a longtime mentor in the world of academic economics. Representative Cathy McMorris Rodgers, Republican of Washington, can still list the women — Ms. Gillibrand and Debbie Wasserman Schultz, both Democrats, among them — who helped plan a baby shower for her oldest child, Cole, who is now 12.

In turn, the women hope to become models for the next generation — aiming to shape policy with their perspectives and to inspire other mothers to follow in their footsteps.