Washington (CNN) Rep. Tulsi Gabbard's clash with 2016 Democratic nominee Hillary Clinton has suddenly thrust her struggling 2020 presidential campaign into the spotlight.

The heated back-and-forth with Clinton, who said Gabbard was a favorite of the Russians and was being groomed for a third-party run, has also raised questions about Gabbard's goal and future in Democratic politics.

The Hawaii Democrat is staring down an increasingly difficult path to the Democratic Party's nomination. She has yet to qualify for the next debate in November and has spent all of the primary race so far at single digits in the polls. Back at home, she also faces the most formidable challenge to her House seat since she was elected in 2012.

Since her first election, Gabbard has enjoyed healthy margins of victory. She had primary challengers in both 2016 and 2018, but still captured more than 75% of the vote in each election. Gabbard was elected in 2012 in a five-way primary race with 54% support.

But local insiders say a primary challenge from state Sen. Kai Kahele is to be taken seriously, in part because he already has high-profile support among towering local officials.

That includes three former governors in the local Democratic establishment: Neil Abercrombie, Ben Cayetano and John Waihee, who don't often appear as a bloc.

"That gives a pretty good indication of how the mainstream Democratic Party here regards her," said Colin Moore, director of the Public Policy Center at the University of Hawaii.

Kahele told CNN on Monday that his campaign had its best day of fundraising when Gabbard and Clinton clashed.

Gabbard has not formally announced a reelection bid for her House seat. Candidates have until June 2, 2020, to file for that November's election.

Some Hawaii political insiders have quietly speculated that Gabbard could be eyeing a cable news contributor deal, but publicly it remains just speculation.

"If you decide to run for the presidency and spend all this time out there, it seems something else other than auditioning for Fox News is in your head," said Neal Milner, professor emeritus of political science at the University of Hawaii.

On television, Gabbard has received a significant amount of coverage from Fox News, where she is often praised for her anti-establishment message. She made an appearance on Friday night with host Tucker Carlson to respond to Clinton and made a plea to Carlson's viewers to support her candidacy.

She often appears on Fox to discuss her foreign policy views, seen as unorthodox by Democratic Party standards. In September, Gabbard was on Fox News defending her statement that President Donald Trump cannot "pimp out" the American military to Saudi Arabia.

For Hawaii political observers who have followed Gabbard's career, her endgame remains a mystery.

"Anyone who says in confidence that they know what she's up to is BS'ing. It's all pretty speculative," Milner said.

"Her relationship with the media is very surface-y," Milner added. "It's very hard to get anything in depth about herself or what she is trying to do."

"It's not as if people in Hawaii have a clear idea of what Tulsi Gabbard wants," said Moore. "Everyone greets it with the same shoulder shrug. We don't know."

For her part, Gabbard, who has vehemently denied Clinton's charges, spent the weekend firing back at Clinton and made it clear her intention is to stay in the primary.

"I am staying in the Democratic Party, and I'm fighting to take our Democratic Party back, out of the hands of Hillary Clinton and the warmongering establishment, and put it back into the hands of the people, so our party can truly be a champion for the people," Gabbard told The Daily Iowan on Friday.

She even turned the Clinton confrontation into a fundraising opportunity, emailing supporters that "I challenge her" to "face me directly."

Sen. Bernie Sanders of Vermont, who Gabbard supported in 2016, defended the congresswoman on Monday, writing in a tweet that "it is outrageous for anyone to suggest that Tulsi is a foreign asset."

The exchange between Gabbard and Clinton also attracted the attention of President Donald Trump, who said Gabbard is "helped" by the allegations. "Hillary Clinton, she's the one that's accusing everyone of being a Russian agent. Anybody that is opposed to her is a Russian agent. That's a scam that was pretty much put down," Trump said at the beginning of a Cabinet meeting on Monday.

He added that he doesn't "know Tulsi, but she's not a Russian agent."

Clinton suggested the Russians were "grooming" a Democrat running in the presidential primary to run as a third-party candidate and champion their interests. The comment appeared to be directed at Gabbard

"I'm not making any predictions, but I think they've got their eye on somebody who is currently in the Democratic primary and are grooming her to be the third-party candidate," Clinton said, speaking on a podcast with former Obama adviser David Plouffe. "She's the favorite of the Russians."

Gabbard is polling at 2% in a September Des Moines Register/CNN Poll and remains far from the threshold to qualify for the November debate. It's possible that October's debate was her final appearance on the stage.

In that debate, Gabbard butted heads with Mayor Pete Buttigieg of South Bend, Indiana, over their foreign policy postures, demonstrating another moment in which she bucked the party's perspective and favored nonintervention. On Sunday, Buttigieg dismissed Clinton's attack, saying "there is no basis for that," and that "statements like that ought to be backed by evidence."

In Gabbard's rural district across Hawaii's outer islands, her anti-establishment streak plays to supporters, especially in a state known for its traditional Democratic Party dominance.

"Part of her support comes from the fact that the Democratic elite don't approve of Tulsi Gabbard. It's something appealing, especially to voters on the neighbor islands," Moore said, using a local term to describe Hawaii's islands other than Oahu.

But Moore noted "how unusual her behavior is as a politician from Hawaii," as especially ambitious and someone who has risen in politics since her election to the state Legislature when she was just 21. "This is a state where people don't step out of line. You wait your turn."

In January, Gabbard disrupted Hawaii's traditionally tight-knit, four-member delegation with a surprise op-ed criticizing Democrats' questioning of a judicial nominee, writing in The Hill that "elected leaders engaging in religion-baiting are playing with fire." Fellow Hawaiian Sen. Mazie Hirono was one of those questioners.

Hirono's office pushed back in a statement, singling out Gabbard by name: "It is unfortunate that Congresswoman Gabbard based her misguided opinion on the far-right wing manipulation of these straightforward questions," Will Dempster, Hirono's spokesman, said in a statement to The Hill in January.

"That is something that is almost never done here," Moore told CNN. "It was greeted with a certain amount of shock by the Democrats here in Hawaii."

Despite that hiccup, the delegation's relationship is outwardly copacetic.

Gabbard's fellow Democratic member of Congress, Rep. Ed Case, said in a statement to CNN that he has a "good and productive relationship with his colleague."