DUBUQUE, Iowa-- O'Rourke-Harris? O'Rourke-Warren?

On Saturday night, at the end of his third day as a presidential candidate, Beto O'Rourke said that he very likely would choose a female running mate if he manages to nab the Democratic presidential nomination next year.

"It would be very difficult not to select a woman with so many extraordinary women who are running right now," he said. "But first I would have to win and there's-- you know, this is as open as it has ever been."

The party's 2016 nominee, Hillary Clinton, would have been the nation's first woman president but she lost to Donald Trump.

Four senators are hoping to break that glass ceiling next year: Kamala Harris of California, Amy Klobuchar of Minnesota, Elizabeth Warren of Massachusetts, and Kirsten Gillibrand of New York. So is Rep. Tulsi Gabbard of Hawaii.

"It's presumptuous for me to think about who I would select as a vice president. Right now I'm seeking the nomination," O'Rourke said. But if he did win, he's well aware that intraparty pressure to avoid and all male ticket would be hard to resist.

Sen. Cory Booker of New Jersey said last month that he would be "looking to women first" when choosing a running mate. In New Hampshire on Friday he predicted that Democrats will nominate a woman for president or vice president next year.

O'Rourke, a three-term congressman from El Paso, made the comments at a campaign stop in Dubuque. As he was leaving a man attending the house party buttonholed him and, with a scrum of news media nearby, loudly insisted on a commitment that if he wins he would pick a woman as his running mate.

"That would be my preference," O'Rourke said.

But he quickly added that it would be presumptuous to make such a promise so early in such a competitive race.

Moments later he was asked again about his veep plans and he told reporters much the same thing.

Geraldine Ferraro, then a congresswoman from New York, made history as the first nominated for vice president by a major party, when Walter Mondale chose her as his running mate in 1984. But they lost, as Ronald Reagan was reelected.

Sen. Ted Cruz, who narrowly defeated O'Rourke last fall, would have had a female vice president if he'd managed to beat Trump in the 2016 primaries. In a desperation move, Cruz announced that former HP chief executive Carly Fiorina would be his runningmate. But the hypothetical ticket evaporated within days when Trump beat him in Indiana and drove him from the race.