“This morning, I changed a diaper before I got on a plane,” said Mr. Swalwell, of California, who has a 2-year-old son and an 8-month-old daughter. “Last night, I came back for bath time. I generally do the wake-up, get them out of their pj’s, change the diaper and feed them.”

It is a shift that reflects changing American expectations around what, exactly, makes a good dad. While academic research and survey data show that female candidates still confront a steeper double standard when it comes to their family life, male politicians with young children suddenly find themselves facing something totally new — a standard.

“Bill Clinton had a youngish daughter but there was no discussion about what his life was like as a parent,” said Jill S. Greenlee, a political science professor at Brandeis University who studies attitudes toward parenthood. “Now these men need to acknowledge their role as fathers, in part, because to ignore it would be potentially harmful to their candidacy.”