That led to jeers on social media, and a bit of confusion — Ms. Ayotte has yet to officially endorse Mr. Trump, although she has said she would vote for him.

“I misspoke tonight,” Ms. Ayotte said in a statement several hours later. “While I would hope all of our children would aspire to be president, neither Donald Trump nor Hillary Clinton have set a good example, and I wouldn’t hold up either of them as role models for my kids.”

Her attempt to walk back her debate comments did not quiet her Twitter critics.

“Trump just spent a week fat-shaming a woman and bragging about not paying taxes,” one wrote. “Kelly Ayotte calls him a role model.”

Added another: “Kelly Ayotte says ‘Donald Trump is absolutely a role model for kids.’ She’s right, kids don’t pay taxes either.”