The group No Labels has said it would be open to the possibility of Haley leading its ticket as it scrambles to find a candidate to top its ticket.

Haley, for her part, has brushed off the No Labels speculation, arguing her place is in the Republican Party. She is also coming off her first primary victory after winning the GOP nominating contest in Washington, D.C. on Sunday.

But with a general air of uncertainty surrounding her endgame in the presidential race, Haley is spurring talk of a possible third-party insurgent bid.

“My heart wishes it was possible but my brain doesn’t think it can be done,” said Tucker Martin, a veteran Republican strategist. “Gov. Haley, she is the embodiment of the conundrum of the modern Republican Party, which is she is exactly who Republicans should be running.”

Polling has consistently shown Haley beating President Biden in a hypothetical match-up. It also shows Americans are unhappy about the idea of another Trump vs. Biden match-up, with many voters pointing to their age. The discontent with the likely rematch has led to speculation about an alternative, particularly on the GOP side.

On Friday, Haley threw cold water on the possibility of a No Labels bid, saying she was a Republican and would not want to run on the group’s proposed unity ticket with a Democrat.

“If I were to do No Labels, that would require a Democrat. I can’t do what I wanted to express with the Democrats,” Haley told reporters.

“I’ve always believed if you do something, do it right or don’t do it,” she said. “And so I don’t think I can do it right. If I ran for No Labels, that would mean it’s about me. It’s not about me. It’s about the direction I think the country should go.”

Last month, No Labels national director Joe Cunningham raised eyebrows when he said Haley was “somebody we’d definitely be interested in.”

Some Republicans have said No Labels was purposefully stirring the speculation about Haley. In a statement on Friday, the group said it had not talked to the former South Carolina governor.

“We have not had contact with Nikki Haley or anyone from her campaign,” said No Labels chief strategist Ryan Clancy. “Late next week, after the Super Tuesday primaries, we will gather our 800 delegates from all 50 states to discuss the path forward for our effort.”

Haley’s Friday remarks came after she said Monday she had not thought about an independent run.

“I’m a Republican. I have not talked to any other organization. I have not put a second of thought into an independent run because I’m a Republican. That’s what I’ve always been,” Haley told Fox News.

The speculation comes amid growing questions over Haley’s reasoning for staying in the race as she heads toward what is expected to be a brutal Super Tuesday for her.

Haley has said that if she were to drop out of the race now, it would be the longest general election in U.S. history. She said Republican primary voters deserve a choice, “not a Soviet-style election with only one candidate. And I have a duty to give them that choice.”

And despite losing the funding from the political network Americans for Prosperity, which is financed by GOP mega-donor Charles Koch, Haley’s campaign says it is still seeing a cash flow. On Friday, the campaign announced it raised $12 million in February.

“Money is a driving force in politics,” Wilson said. “AFP was a huge force in pushing Haley’s name out and getting it in front of the voters. Without that, I think she’s hoping that her name ID alone may carry her.

Haley also got another potential boost on Friday when she received Sen. Lisa Murkowski’s (R-Alaska) endorsement ahead of the state’s caucuses on Tuesday. Murkowski, a vocal Trump critic, is the first sitting senator to endorse Haley.

Republican strategists and operatives repeatedly point to the unity pledge Haley signed to support the party’s eventual nominee. Last August, Haley signed a pledge required by the Republican National Committee to support the party’s eventual nominee. Signing the pledge was part of the criteria needed to participate in the first GOP primary debate.

“To go against that would come back and be political blowback for the long haul that I think at 52 and her first run for national politics would be very dangerous for her political future,” Wilson said.

Wilson said there is precedent for the losing Republican candidate to endorse the eventual nominee after a fight and that it could pay dividends.

“We’re at the same place we were in 1976,” he said. “Ronald Reagan supported the eventual nominee, Gerald Ford. He actually called for unity of the party after a pretty contentious floor fight and then was seen as the heir apparent after the years of Jimmy Carter.”

“If Haley’s playing a long game, then she’s got to start playing the long game,” he added.

There’s also the logistical question of launching a third party, which is normally seen as a spoiler in U.S. presidential politics, this late in the game.

“You’re talking 50 different sets of rules and laws, which is the way we’re set up as a country,” Wilson said. “That’s a lot of work that has to be done and we haven’t seen a real third-party candidate mount a real campaign since the days of Ross Perot.”

Independent candidate Robert F. Kennedy Jr. announced on Thursday that he would appear on the ballot in Hawaii in November, but still has a long way to go on the map. The super PAC backing Kennedy said this week it has collected the requisite number of signatures for Kennedy in Georgia and Arizona. A spokesperson for Kennedy’s campaign did not independently verify the signature tally for those two states.

“There may be an appetite for a third party but the question is will somebody actually order the dish?” Wilson said.

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