Mr. Biden said he was satisfied with his debate performance, which was widely criticized. He dismissed several polls taken in the aftermath of the back-to-back forums that show his once-solid lead evaporating.

“I’m still way ahead,” he said.

Mr. Biden is not the only candidate struggling with how to talk about school integration. After Ms. Harris found success confronting the former vice president on busing, she has appeared uncertain how to characterize her own views on the matter.

Before addressing a July 4 house party in a sweltering backyard in Indianola, Iowa, Ms. Harris insisted that she and Mr. Biden did not share the same position on federally mandated busing. She then attempted to focus the conversation in the past rather than the present.

“I have asked him and have yet to hear him agree that busing that was court-ordered and mandated in most places and in that era in which I was bused, was necessary,” Ms. Harris said of her childhood in Berkeley, Calif., in the late 1960s and 1970s. “He has yet to agree that his position on this, which was to work with segregationists and oppose busing, was wrong.”

Ms. Harris was asked to explain what she meant when she said Wednesday that busing should be part of “the toolbox” to address desegregating schools, which would be distinct from a federal mandate. She suggested that the environment around civil rights is different today from when she was a student, though she said she supported school districts and municipalities doing “whatever they need to do” on integration measures.

This is not the first issue on which Ms. Harris has muddled her response — she has also struggled to articulate whether she thinks private health care should be eliminated — but the California senator dismissed questions about her consistency.