Last Friday, at Representative James Clyburn’s fish fry in Columbia, South Carolina, I met Sharon Hamill, a 59-year-old insurance agent who was still deciding whom to support in the Democratic primary. She told me she liked Elizabeth Warren, “but I don’t think that this is the year for a woman president.” After Hillary Clinton’s defeat, she feared that a female candidate would be unelectable, and said she thought voters wanted a president who wouldn’t inspire a furious backlash. She was leaning toward Joe Biden, even though she worried about his age.

I’ve heard similar things from other women on the campaign trail. Clinton’s loss was a trauma that they’re terrified to re-enact. “I like Warren. I like Kamala,” 63-year-old Shyvette Brown told me at the Biden campaign’s kickoff rally in Philadelphia in May. “But I just don’t think they will elect a woman.” She didn’t like it or think it was fair. She just thought it was true.

We’ve now had two Democratic debates in which women dominated. On Wednesday, Warren was one of the first debate’s clear winners, along with Cory Booker. And across the political spectrum, there was a near-universal consensus that Kamala Harris triumphed on Thursday, scoring a devastating blow against Biden in an exchange about busing. The question now is whether these victories can convince battle-scarred Democratic women to believe once again that a woman can beat Donald Trump.

[Listen to “The Argument” podcast every Thursday morning, with Ross Douthat, Michelle Goldberg and David Leonhardt.]