Introducing former President Donald J. Trump at a town-hall event in Michigan on Tuesday, Gov. Sarah Huckabee Sanders of Arkansas extolled the virtue of humility in politics with an amusing story: She once teared up while watching her daughter get ready for a father-daughter dance, and her daughter said, “It’s OK, Mommy, one day you can be pretty too.”

“So my kids keep me humble,” Ms. Sanders said. Then, mispronouncing Vice President Kamala Harris’s name, she added, “Unfortunately, Kamala Harris doesn’t have anything keeping her humble.”

The comment was widely interpreted as a reference to Ms. Harris not having biological children; she has two stepchildren. Coming from a surrogate for a campaign whose vice-presidential nominee, Senator JD Vance of Ohio, has been criticized for his past description of Democratic leadership as “childless cat ladies,” Ms. Sanders’s remark quickly prompted bipartisan backlash, including from Bryan Lanza, a senior adviser to the Trump campaign.

Mr. Lanza said on CNN that the remark was “actually offensive” and that he was “disappointed in Sarah.”

Several Democratic-aligned groups highlighted the remark on social media, including the super PAC American Bridge 21st Century, Young Democrats of America and Republican Voters Against Trump. So did TV commentators.

“Whoa,” Mika Brzezinski said on MSNBC’s “Morning Joe” on Wednesday. “What is their obsession with women without children of their biological connection?”

A spokeswoman for Ms. Sanders did not immediately respond to a request for comment. Neither did Ms. Harris’s campaign.

Kerstin Emhoff — the ex-wife of Ms. Harris’s husband, Doug Emhoff, and the mother of Ms. Harris’s stepchildren — defended Ms. Harris.

“Cole and Ella keep us inspired to make the world a better place,” she said in a social media post, referring to her children. “I do it through storytelling. Kamala Harris has spent her entire career working for the people, ALL families. That keeps you pretty humble.”

Mr. Vance has raised eyebrows on the matter of parenting before. In 2021, he said that perhaps parents “should have more of an ability to speak your voice in our democratic republic than people who don’t have kids,” a suggestion that he later said was a “thought experiment” and not serious.

He has also said he wasn’t disparaging women without children, while doubling down on describing Democrats as “anti-family.”

His “childless cat ladies” remark has become something of a cultural phenomenon among supporters of Ms. Harris. In one sign of its continuing resonance, Taylor Swift used it to sign off her endorsement of Ms. Harris last week.