Americans have grown accustomed to observing female leaders elsewhere, including Margaret Thatcher and Theresa May in Britain, and Angela Merkel in Germany. At home, the Democratic pollster Peter Hart said, the rise of some women to the top of major corporations smoothed a path for voters to envision a woman in the Oval Office.

“There is much greater acceptance of women being able to be seen in that commander-in-chief role,” Mr. Hart said. He advised the 1984 presidential campaign of Walter Mondale, who picked Mrs. Ferraro as his running mate.

Mrs. Ferraro, then in her sixth year in the House of Representatives, didn’t shrink from the “let me help you” barb in her debate. “I almost resent, Vice President Bush, your patronizing attitude that you have to teach me about foreign policy,” she shot back.

Mrs. Clinton need not fear that line of argument. In the poll Mr. Hart helps conduct for NBC News and The Wall Street Journal, voters last month preferred her over Mr. Trump by 26 percentage points on conducting foreign policy, 18 points on handling a crisis, and 11 points on serving as commander in chief.

Nor does Mrs. Clinton, whose truthfulness was called into question most recently over her use of a private email server while she was secretary of state, benefit from any presumption of honesty. Just 22 percent of voters in the NBC-Wall Street Journal poll rated her highly as “honest and straightforward,” the sort of finding that Mr. Trump has worked to exploit by frequently referring to her as “Crooked Hillary.”

Mr. Trump has also sought to attack Mrs. Clinton by suggesting that the success of her campaign is rooted almost entirely in her gender.

“If Hillary Clinton were a man, I don’t think she’d get 5 percent of the vote,” he said last spring. “The only thing she’s got going is the women’s card.”