Privately, Democratic strategists, candidates and officials say they’ve been alarmed by how deeply doubts about female electability have taken hold. In polling, interviews and focus groups, a portion of the party’s voters suggest they’re eager to see a woman on the ticket but fear that putting her in the top slot could cost them the White House — again. The question comes up frequently in early primary states, including at events organized for female voters.

Much of the concern centers not on what Democratic voters themselves say they want but a prediction of what they believe others will support.

That left the women in the race with a considerable challenge for last week’s debates: introducing themselves to voters while also finding a way to tackle the lingering doubt that this country would elect a female president.

Immediately after the debate, strategists said they succeeded, arguing the six women onstage left little doubt that a woman could win.