Mr. Swalwell said he tries to spend no more than five consecutive days away from his children. His family relies on his wife’s aunt, who lives with them, and an additional babysitter to help with child care. Like the candidate, his wife also frequently travels for her job. “It’s a day-to-day challenge to make the child care part of it work,” he said. “We just can’t afford to not have both of us work.”

Fathers are far from the only ones talking loudly about the emotional and financial struggles of balancing work and family responsibilities. Senator Elizabeth Warren frequently tells the story of her 78-year-old Aunt Bee, who moved into her house after her divorce in 1978 to help care for her children, allowing her to keep working as a law professor.

Senator Kamala Harris has written about the pain of missing her stepdaughter’s high school graduation to question the former F.B.I. director James B. Comey at a congressional hearing. And Senator Amy Klobuchar attributes the start of her political career to getting kicked out of the hospital 24 hours after giving birth to her daughter, who was born with a medical condition.

Senator Kirsten Gillibrand, whose two sons are 15 and 11, has placed the working mom juggle at the center of her pitch to voters, promising to “fight for your children as hard as I would fight for my own.” She has on occasion asked female reporters with young children who are covering the campaign if their husbands work. She understands the logistics challenge: Her husband is staying home in Washington with the children during the presidential campaign, though the entire family plans to spend much of the summer in upstate New York where her campaign is based.

Ms. Gillibrand is the only woman to run for a major party’s presidential nomination with school-age children at home, a fact that reflects the reality that women have typically entered politics at a later age than men. Women waited until their kids were grown to run for office, like Hillary Clinton, or, if they did not wait, were urged to tamp down talk of their family lives.

That began to change with the 2018 midterms, when a new crop of younger female candidates publicly embraced their role as mothers, arguing that their family life made them more qualified — not less — for political office.

After many won, they set out changing the culture of Congress, creating an informal “mom caucus” to call for changes like shifting the scheduling of votes earlier to better accommodate child-care needs.