An edited, four-minute video of Ms. Fabian’s exchange with the judges posted by NowThis News on Twitter has been viewed more than 20 million times.

Ms. Fabian stopped short of directly stating that the government did not have to provide toothbrushes, soap and beds to migrant children. But her attempts to dance around the subject, and her apparent inability to clarify for the judges just what she was arguing, helped turn Ms. Fabian into the public face of the Trump administration’s treatment of migrant children at the border.

“Don’t let her be anonymous,” one Twitter commenter posted. “Whenever anyone searches her name for the rest of her life, let them discover that Sarah Fabian doesn’t believe children need blankets, soap, or toothbrushes.”

A spokeswoman for the Justice Department confirmed that Ms. Fabian has received death threats but did not respond to requests for an interview. In a private message on Facebook, Ms. Fabian expressed regret to her friends, acknowledging that her words had “struck a nerve.”

“Maybe many nerves,” she wrote, according to screenshots of the message provided to The New York Times on Tuesday by two of her Facebook friends. “I’m so sorry that happened and I wish I could go back and try to say something better to make the position more clear, and since I can’t lots of people may well hate me for a long time. I get it, and I accept it, and I’m not going to try in vain to fight back against that other than to try to look out for my own safety and to hope that people take it easy on my family.”

Ms. Fabian stressed that she was neither a political appointee nor “an official of any administration,” and that she believed many people mistakenly believed she was in court arguing against providing hygiene items to children.

“Whether that’s because people saw only certain clips of the argument, or because the nature of oral argument is that sometimes your positions don’t come out in full, or because I never articulated some pieces of my argument well enough to make my position clear, I can’t say,” she wrote. “Probably all of those. I do not believe that’s the position I was representing, and I get that defending myself by parsing out a technical legal position won’t change most people’s minds.”