“Now, men say: ‘Well, you have a great résumé, but you’re kind of an insider,’” Ms. Mills said, to groans from a predominantly female crowd of about four dozen. “Really? For decades, men were telling women: ‘Just a little more experience and you’ll be qualified.’”

She finished with gusto: “Well, goddamn it, I am qualified!”

A year and half after Hillary Clinton failed to win the highest executive office, there have been a few signal victories for Democratic women in governor’s races: Stacey Abrams in Georgia became the first black woman ever nominated for governor there, defeating another woman in May. Representative Michelle Lujan Grisham of New Mexico dispatched male opponents in a Democratic primary last week to become her party’s first Latina nominee for governor, and women have been nominated in longer-shot races for governor in Texas and Idaho.

But in several of the biggest states on the map, women have strained to break through or appear at risk of falling behind. Some may win despite being outspent by male opponents, but the financial disparity points to the lingering institutional barriers confronting female candidates who try to crack the glass ceiling of the statehouse dome.

“You can’t wait to be asked because a lot of guys won’t ask you,” said Kathleen Sebelius, the former Kansas governor. “You have to crash the party and, if there’s an opening, go for it because a lot the party organizations are run by the old boys.”

Ms. Sebelius helped recruit a female protégé, Laura Kelly, to run for governor in her home state. But there are relatively few former female governors to clear the path for others. While women have led major states in the past — such as Ann Richards in Texas, Janet Napolitano in Arizona and Christine Todd Whitman in New Jersey — only four serve as governors today, two of whom inherited the job after male governors resigned. Twenty-two states, including Nevada and Maine, have never had a female chief executive, according to the Center for American Women and Politics at Rutgers University.

State capitols remain dominated by self-perpetuating male political networks that determine who is groomed and promoted — and the outsiders who do force their way into the nominating process are often rich men wielding fortunes.