Senator Manchin is traveling to New Hampshire for an event focused on putting up a third-party candidate for the presidency just as his most formidable opponent for his Senate seat, Governor Justice, has announced that his campaign has raised almost $1 million, a large haul for West Virginia.

This Monday, Mr. Manchin will be at an event for No Labels, which is courting him as a potential third-party presidential candidate in 2024. Mr. Manchin, who stepped down as the honorary co-chairman of No Labels in 2014, has refused to answer whether he will seek re-election in West Virginia in 2024.

The conservative Democrat has stated that he “will win any race” he enters. Between his longtime practice of announcing his candidacy at the last possible opportunity and this promise, there has been no shortage of speculation on whether Mr. Manchin’s next move will be seeking re-election to the Senate, the presidency, or retiring.

Although Mr. Manchin’s chances of winning the presidency would be low, he would certainly be able to influence the race. Some polls suggest that he could deliver the race to President Trump in with President Biden, with a June Echelon Insights survey showing Mr. Manchin carrying 9 percent of the vote to Mr. Trump’s 42 percent and Mr. Biden’s 41 percent.

In a matchup between Mr. Biden, Governor DeSantis, and Mr. Manchin, the survey found that the candidates would carry 42 percent, 38 percent, and 8 percent. Without Mr. Manchin in the mix, the pollster found that Mr. Biden leads Mr. Trump by two points and Mr. DeSantis by four points nationally.

It would only be the latest example of Mr. Manchin confounding Mr. Biden at every step. He personally blocked much of Mr. Biden’s ambitious domestic agenda as one of two Democratic senators who refused to vote in lock-step with the party in the 50-50 Senate of 2021 and 2022.

Now, the prospect of a spoiler candidate like Mr. Manchin combined with No Labels receiving significant funding from large Republican donors, according to the nonprofit Influence Watch, has elicited blowback from Democrats.

In response, the Democratic co-chairman of No Labels, Ben Chavis, told NBC News that the organization “is not and will not be a spoiler in favor of Donald Trump in 2024.”

“If we find that the polls are changed and Joe Biden is way, way out ahead, and the person who the Republicans may choose — and if they continue to choose Donald Trump, even though he’s been indicted — then No Labels will stand down,” Mr. Chavis said.

As Mr. Manchin heads to New Hampshire, Mr. Justice’s campaign announced its fundraising haul for the second quarter of 2023, $935,000.

Although relatively modest by the standards of some recent Senate competition — the 2022 election in Georgia saw more than $1.4 billion in political spending — the fundraising is significant in deep-red West Virginia.

In 2018, the Senate race in the state saw just more than $15 million raised by the candidates. Mr. Justice’s campaign manager, Roman Stauffer, touted the new figure, saying, “In only 64 days, with no prior federal fundraising experience, Governor Justice raised nearly $1 million.”

“Governor Justice has received tremendous support from West Virginians and those who have confidence in his leadership and conservative record of achievements in West Virginia,” Mr. Stauffer added.

Mr. Justice’s chief primary opponent, Representative Alex Mooney, hasn’t announced his second-quarter fundraising but did raise about $500,000 in the first quarter.

An influential anti-tax group, Club for Growth, also injected $10 million into Mr. Mooney’s campaign to help him defeat Mr. Justice in the primary, meaning the GOP primary in the state may see nearly as much spending as the 2018 general election.

The West Virginia Senate race is expected to be a major battleground, probably being the best opportunity for Republicans to flip a seat in 2024. The Cook Political Report rates it as a “toss up.”

This is even though Mr. Justice in recent polls has posted commanding leads over Mr. Manchin. A May East Carolina University Center for Survey Research poll found that Mr. Justice leads Mr. Manchin by 54 percent to 32 percent in a head-to-head matchup.

Mr. Manchin, though, has always defied the odds, first winning office in a 2010 special election against businessman John Raese, only two years after Senator McCain carried the state by 13 points in the 2008 presidential election.

In 2018, Mr. Manchin won by three points against Attorney General Patrick Morrisey just two years after Mr. Trump carried the state by 42 points.