”I just think she has the moxie to bring it to the Donald”

Together, the two senators have functioned as something of a political pincer, squeezing Mr. Biden and Mr. Sanders from the left and the relative center, and endangering any hope of an easy march to victory for either man.

After Ms. Harris’s searing clash with Mr. Biden over his record on race in the first primary debate, she claimed for herself a chunk of Mr. Biden’s formidable support among African-Americans and white liberals. And Ms. Warren, with her relentless focus on economic inequality and political corruption, and her full portfolio of progressive policy proposals, has cut deeply into the coalition Mr. Sanders built during his 2016 campaign.

Their performances in the first debate lifted both women, with Ms. Harris making an especially sharp ascent after confronting Mr. Biden — a showdown that convinced some voters she had the toughness necessary for the general election.

”I just think she has the moxie to bring it to the Donald,” said Claire Haws, a stay-at-home mother from Des Moines, who contributed to Ms. Harris’s campaign after watching her in the debate.