And if they settle on a man, can they still be the party of gender diversity?

Just how hazardous these dilemmas may prove in the Democratic contest became clear on Wednesday, when John Hickenlooper, the former governor of Colorado, was asked what is becoming a stock question for men seeking the Democratic nomination: whether they would choose a female running mate if they thwarted plans for a female standard-bearer.

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“Of course,” the mild-mannered 67-year-old centrist, who went from geologist to brewer to politician, told CNN’s Dana Bash in a town hall in Atlanta. He would have a bevy of options. Already six women are White House contenders.

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Then he tried to flip the script, succeeding mainly in illustrating how fraught the gender politics of the Democratic primary are shaping up to be.

“Well, I’ll ask you another question,” he said. “But how come we’re not asking, more often, the women, ‘Would you be willing to put a man on the ticket?’”

The remark elicited what sounded like a shout of disapproval from the audience. Many observers — including members of the media in Denver, where Hickenlooper got his political start as mayor — interpreted the query as tone-deaf, revealing a lack of sensitivity about the historic underrepresentation of women in politics.

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On Twitter, the statement was termed a “hickenblooper.”

After the event, the Democrat told a CNN reporter that he had intended to criticize the premise of the question, which he said discounted a woman’s chances of rising to the top of the ticket — and therefore facing the vice president choice herself. “People can take it out of context,” he said. In response to a request from The Washington Post, a campaign spokeswoman pointed to the candidate’s clarification.

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Whether his observation was ahead of the curve or woefully behind, it spoke to Democratic sensitivities about the cause of gender diversity. So, too, it captured a fierce debate about contrasting expectations for male and female political aspirants, now expected to broadcast their intimate lives on social media as they compete for the chance to try their hand against a president who became famous on reality television. These questions have taken on new significance as a record-breaking number of female candidates seek the Democratic nomination, following the historic number of women who entered midterm races last fall.

Hickenlooper, who is barely registering in early polls, is not alone in being asked whether he would put a woman on the ticket.

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Sen. Cory Booker of New Jersey was unequivocal in an appearance Wednesday on “The Ellen DeGeneres Show.”

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“We should be a ticket that reflects the diversity of this country — gender diversity, race diversity," Booker, 49, said. "And if I am elected as the nominee, I’m going to make sure there is gender diversity on the ticket.”

Part of his motivation, he explained, owed to the fact that he “wanted there to be a woman president in 2016. It’s unfortunate that there wasn’t.”

Some of his male competitors have signaled that they are thinking along similar lines but declined to make a commitment.

Beto O’Rourke, the former Texas congressman whose failed Senate bid last year drove historic turnout among minorities and young voters, was pressed by a voter on Saturday after a house party in Dubuque, Iowa, about picking a woman to be his running mate.

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O’Rourke, who entered the presidential race last week, has already learned a lesson about the centrality of issues of representation in the crowded Democratic field. He was forced to apologize on Friday for joking on the campaign trail that his wife was raising their kids, “sometimes with my help.” Showing contrition during the taping of a podcast in Cedar Rapids, Iowa, he said, “I have enjoyed white privilege.”

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As O’Rourke, 46, considered his response about a potential running mate, a woman off-screen chimed in, “I need a job.”

“It’s hard for me to see a reason why I would not do that,” said O’Rourke, who raised more than $6.1 million on the first day of his campaign. “But talking about who I would pick as vice president just feels really premature.”

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The man in Dubuque continued to press the candidate, saying a woman needed to be on the ticket.

“I hear you. Again that would be my preference,” O’Rourke said. “I feel like it would be very presumptuous for me to talk about who I would select as vice president right now. But your point is taken.”

And in February, Sen. Bernie Sanders, the Vermont Independent who lost a spirited primary bid to Clinton in 2016, said he would aim to balance out the ticket, in terms of not just gender but also age.

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"I think we would look for somebody who is maybe not of the same gender that I am, and maybe somebody who might be a couple of years younger than me,” the 77-year-old said in an appearance on “The Young Turks,” a progressive online news show.

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Beyond gender and racial diversity, Democrats are also grappling with a generational question — whether to send someone of President Trump’s age cohort into the ring with him, or whether to put forward a fresher face. The party has an opportunity to nominate a millennial in Pete Buttigieg, the mayor of South Bend, Ind., who would also be the nation’s first gay president.

Buttigieg, 37, has denounced Vice President Pence, who hails from his home state, as a “cheerleader of the porn star presidency,” but hasn’t confirmed the demographic profile of the person he would choose to be his No. 2.

Matt Viser contributed to this report.