Ed Privé cannot vote for Congresswoman Tulsi Gabbard in New Hampshire's primary on February 11th. A registered Republican, the 69-year-old may only vote for candidates belonging to the GOP in a contest President Trump is all but certain to win. But that did not stop him from attending one of the Hawaii congresswoman's town halls in December.

"Honestly, I disagreed with Trump, but I voted for him," Privé said. "I'm here now because she makes sense. The rest of them don't."

Privé, a Marine Corps veteran, voted twice for President Obama before casting his ballot for Mr. Trump in 2016. He's the kind of swing-voter that Democrats are desperate to win back in November. And he says Gabbard is just the kind of candidate who could make that happen.

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Lingering on the edge of the photo line, Privé exhaled. "She doesn't want to give away the farm, but she wants to help people."

"And if she were to be the nominee of the Democratic Party, I would have a very difficult time voting for Trump," Privé added.

Tulsi Gabbard with Ed Privé in Northfield, NH Nicole Sganga

Gabbard's long-shot campaign for the presidency is betting big on a strong performance in New Hampshire, where the primary historically rewards outsiders and underdogs, on occasion. Over 42% of the state's voters here are registered as "undeclared," which allows them to vote in either party's primary in February. And while other candidates focus on next week's Iowa caucuses, Gabbard has all but moved to New Hampshire, spending more days in state (a sum total of 34) than any other Democratic candidate across December and January.

Gabbard, a 38-year-old Iraqi War veteran who backed Bernie Sanders in the last Democratic primary, fuses progressive policy stances with the kind of patriotic displays sometimes more associated with Republican campaigns. Before she makes her hour-long pitch to voters at rallies throughout New Hampshire, her audiences are often instructed to stand for the pledge of allegiance or bow their heads for a moment of silence.

A recent analysis by the New York Times reveals just one-fifth of Obama-Trump voters returned to the Democratic Party in the 2018 midterm elections, while three-quarters voted Republican.

Toby McIntire, a former Army captain, says she first became aware of Gabbard after spotting one of her "huge billboards" off of Interstate 95. Before long, McIntire and her wife Katie Duffey were hosting a house party for Gabbard to introduce the congresswoman to their friends and neighbors.

Tulsi Gabbard speaks at a rally in Merrimack, NH. Nicole Sganga

McIntire, however, is a Republican who says she will vote for Mr. Trump if Gabbard isn't the Democratic nominee. "I'm not going to lie. His messaging of 'Make America Great Again' and defense of the country, from a military perspective, resonated with me."

That is the double-bind of Gabbard's candidacy. She appeals to some independent voters Democrats are anxious to win in the general election, but not many party stalwarts. In a Boston Globe/Suffolk University poll released earlier this month, Gabbard earned 5% support among likely New Hampshire Democratic primary voters. But among independents, Gabbard is the first choice for a whopping 21%.

Roughly half of the New Hampshire towns Gabbard has visited backed Mr. Trump in 2016. Her populist, anti-war message attracts fans from both ends of the political spectrum, including former Trump strategist Steve Bannon and former Democratic Ohio Congressman Dennis Kucinich. But she has struggled to attract much of any support from mainstream Democratic voters who pick their party's nominee.

While her chances of winning the primary are extraordinarily slim, national Democrats are worried that Gabbard could still find a way of spoiling their chances of beating Mr. Trump. Some have even gone so far as to insinuate the combat veteran, who infamously met with Syrian dictator Bashir al-Assad in 2017, might be the agent of a foreign power.

Tulsi Gabbard speaks during a panel with former Ohio Representative Dennis Kucinich and Stephen Kinzer, and moderated by Lawrence Lessig in Concord, NH. Nicole Sganga

In an apparent reference to Gabbard, 2016 Democratic presidential nominee Hillary Clinton suggested late last year that the Russian government is "grooming" a candidate for a third-party run to disrupt the 2020 election. Gabbard is now suing Clinton over the remark for a lump sum of $50 million.

For her part, Gabbard, who is not running for re-election to the House, has repeatedly insisted that she will not run as an independent or third-party candidate in the general election. But if Gabbard were to change her mind, Steve Bannon told CBS News, her appeal to Republicans and Republican-leaning voters is so intense it might actually help Democrats reclaim the White House.

"[S]he's pulling from Trump voters. It could make it even tougher for Trump to win, particularly in states like Michigan and New Hampshire," Bannon told CBS News.

"Clinton doesn't get it — she thinks she's a Russian asset or something of a spoiler for the Democrats. As usual, Clinton misses the point. It shows you how out of touch she is. These are Trump voters going to see her. They're not democratic voters. Or they're Democrats who voted for Trump. Or independents who voted for Trump."

Bannon, who calls Gabbard "beyond a rock star" and a "real populist-nationalist," invited the congresswoman to meet with Trump officials after the 2016 election. "She's one of the first people we got up there. I was just blown away by her level of sophistication on national security and her understanding of 'America First,'" Bannon said.

Dennis Kucinich, who ran for the presidency twice as a stalwart progressive, is one of Gabbard's left-leaning supporters. "Tulsi is one of the few individuals who provides a categorical challenge to U.S. foreign policy...She can appeal to both libertarians and Republicans. That's a winning approach," he told CBS News.

First, however, Gabbard needs to find a way to win over Democrats. The Hawaii lawmaker has not qualified for the debate stage in months, and while other candidates' boast hundreds of staffers and dozens of offices in key early states, Gabbard employs a team of just over a dozen paid employees nationwide, according to FEC filings. The campaign opened up their very first field office earlier this month in downtown Manchester, operated by a round of 50 full-time volunteers in New Hampshire.

To vote or not to vote for Gabbard is not a question for Republican Brian Lindsay of Hudson, NH. The lifelong Republican committed to casting his ballot for Trump in November, but agreed to tag along with his teenage girls to the candidate's town hall.

Lindsay liked what he saw. "Hands down, she should be the democratic nominee. I think the others are a bunch of crackpots," he volunteered. "She's not really one of them. A little less abrasive."

He paused. "Much less abrasive."