They are the stragglers in the Democratic presidential race — down in the polls and excluded from this week’s debate in Houston but vowing to keep running.

Ask why they refuse to call it quits, and many of the stragglers will tell you they are leading “a movement.”

Rep. Tulsi Gabbard of Hawaii, who is stuck in the low single digits in the polls, said those calling for her to give up just don’t understand what her anti-war campaign is all about.

“Are you quitting? Hell, no,” Ms. Gabbard, a military combat veteran, declared at a campaign stop in Atlanta.

Ms. Gabbard came close to qualifying for the debate Thursday and in some polls outperforms several of the candidates who have made it onto the stage.

Rep. Tim Ryan of Ohio does not register in the polls and lags in donors, but he said he won’t be deterred by naysayers.

“We know that pundits and Washington elites are claiming that we’re ‘out’ — but we also know the strength, resiliency, and determination of this movement,” he wrote in a fundraising email.

Though stuck at zero in the polls, Sen. Michael F. Bennet of Colorado recently boasted to Democratic Party activists that he is part of the “let’s beat Donald Trump wing of the Democratic Party” and that his purple state pedigree makes him ideally suited to lead the charge.

“People in Iowa, South Carolina and Nevada, I don’t think they’ve made up their minds, and I think this race is wide open,” Mr. Bennet told reporters in Cedar Rapids, Iowa.

Nearly a dozen candidates in the crowded Democratic field soldier on despite having virtually no chance of claiming the nomination.

They refuse to follow the example of Sen. Kirsten Gillibrand of New York, who promptly gave up her White House quest after failing to qualify for the Houston debate.

“I know this isn’t the result we wanted. We wanted to win this race, but it’s important to know when it’s not your time and to know how you can best serve your community and country,” she said in a video posted on Twitter.

She was the fifth major candidate to drop out last month, raising the total to six.

The Democrats have been dropping out sooner than the Republicans did in the 2016 race.

At this time in 2015, none of the 17 candidates had given up. By the end of September, former Gov. Rick Perry of Texas and then-Gov. Scott Walker of Wisconsin quit. Three more bowed out before the Iowa caucuses in February.

New York Mayor Bill de Blasio has put an October expiration date on his hobbling run for the Democratic nomination.

“I think the logical thing to say is I’m going to go and try and make the October debates and if I can, that’s a good reason to keep going forward. If I can’t, I think it’s really tough to conceive of continuing,” he said at a non-campaign event in New York, according to The New York Times.

Those who persevere despite the long odds could be angling for the vice presidential slot or a Cabinet post if Democrats succeed in ousting President Trump. They might hope to raise their profile to run for another office such as senator or governor or land a show on MSNBC.

All of them insist they still have a shot at the nomination, though.

“Part of the reason these candidates have stayed in the race is that they have nothing to lose by sticking with it and little to gain by dropping out,” said University of Virginia professor Jennifer Lawless, who studies political ambition.

Ms. Gabbard and Mr. Ryan are likely headed for easy re-elections to their House seats, and Mr. Bennet is not up for reelection until 2022.

Ms. Lawless said Ms. Gabbard’s craving for a Senate seat is well known and that Mr. Ryan last year made a bid for House speaker and could be positioning himself to try again.

“So why not give it a shot, build some national name recognition and see where it takes them?” Ms. Lawless said. “There are potential upsides to outperforming expectations and demonstrating an ability to compete on a national stage. They’re also not chipping away at any of the top-tier candidates’ support, so there’s no ‘spoiler’ problem.”

New Age author Marianne Williamson’s offbeat campaign has generated buzz but not rising poll numbers. She acknowledged that it is getting more difficult to peel off the “long shot” label that has been applied to her.

“But I’m in it. There are the important — very, very important forces that have to do with the voters, with people,” she said on “America This Week.”

“You don’t get the sense that the voters care about [polls and pundits]. You get the sense that the voters care about the United States of America and what is happening here,” Ms. Williamson said. “You get a sense sometimes that the media is playing one game, that the politicos are playing one and then the voters are in a different place. And that’s the listening I’m speaking into.”

Others such as Miramar, Florida, Mayor Wayne Messam, and retired Navy Adm. Joe Sestak continue to run in relative obscurity.

Millionaire businessman and former Rep. John Delaney of Maryland in July 2017 became the first candidate to enter the race but has struggled ever since. Concentrating his efforts on Iowa, Mr. Delaney hopes for an upset win or at least a surprise finish anywhere near the top in the state’s leadoff caucuses. He is getting 1% of the vote in the Real Clear Politics average of recent Iowa polls.

Mr. Delaney’s estimated net worth of more than $200 million allows him to self-fund his campaign. But his pockets are not as deep as billionaire activist Tom Steyer, who is spending at least $100 million to stay in the race.

Mr. Delaney said he keeps running because he believes he can win.

“When you’ve been in Iowa and New Hampshire as I have and you talk to voters, you realize very few voters are even decided at this point. I think we’re going to have a dramatically changing field. I just think there’s a lot of action left in this primary,” he told The Baltimore Sun.

The Democratic National Committee raised the bar for candidates to get into the party’s third presidential primary debate.

After having 20 candidates in the first two debates, 10 qualified for Houston this week: former Vice President Joseph R. Biden; Sens. Elizabeth Warren of Massachusetts, Bernard Sanders of Vermont, Kamala D. Harris of California, Cory A. Booker of New Jersey and Amy Klobuchar of Minnesota; South Bend, Indiana, Mayor Pete Buttigieg; entrepreneur Andrew Yang; former Rep. Beto O’Rourke of Texas; and former Housing and Urban Development Secretary Julian Castro.

They met both the polling and the donor thresholds, instead of either, as had been enough to make the first two debates. Each threshold also had been raised. Candidates needed 2% in four recognized polls and 130,000 donors across 20 states, up from 1% in polls or 65,000 donors.

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