No Labels is telegraphing its strategy of choosing a Republican as its candidate for president in 2024, claiming to have a path to victory in five swing states. A new survey No Labels is using to back up that claim is setting off a new round of hand-wringing among Democrats and accusations from critics that the group is trying to deliver the election to President Trump.

A recent Harris X poll conducted across eight swing states found that No Labels would have the best chance of winning some states with a Republican at the top of its ticket. The survey found that the No Labels candidate would be competitive in Arizona, Michigan, Nevada, North Carolina, and Wisconsin if there was a Republican at the top of its ticket.

With a Democrat at the top of the ticket, Mr. Trump leads in seven of the eight surveyed swing states — Arizona, Florida, Georgia, Michigan, North Carolina, Pennsylvania, and Wisconsin.

With no third-party candidates on the ballot, the survey found that President Biden leads in Pennsylvania and enjoys a small advantage in Michigan, Nevada, and North Carolina. Mr. Trump leads in Arizona, Florida, Georgia, and Wisconsin under this scenario.

No Labels’s chief strategist, Ryan Clancy, tells the Sun that the group has “done our homework” and that based on its research, “the path for an independent ticket to win the White House is wider now than ever before.”

No Labels and its self-proclaimed “unity ticket” is another potential confounding variable in the 2024 election, as third parties like the Libertarian and Green parties run candidates of their own, and independents like attorney Robert Kennedy Jr. and philosopher Cornel West mount their own efforts.

The new posturing from No Labels has drawn accusations from some critics of the group, like Third Way, which is accusing it of attempting to prevent either Mr. Trump or Mr. Biden from winning 270 electoral votes in 2024.

If no president is elected with a majority in the Electoral College, the president is chosen by the House of Representatives, with each state’s delegation getting a single vote. The vice president would be chosen by the Senate, with each senator getting one vote.

This scenario, called a contingent election, hasn’t happened since 1837. A memo circulated by Third Way argues that No Labels is trying to make 2024 a contingent election.

“No Labels has made clear that their new plan is to put a Republican at the top of their ticket,” the memo reads. “And because they can’t win the presidency outright, they’ve indicated that their intention now is to exercise leverage over the winner by denying both major parties 270 Electoral College Votes.”

The memo goes on to say that a “contingent election in the House would create chaos” that would almost certainly result in the House choosing Mr. Trump. Democrats have not controlled a majority of House delegations since 2008, and even a landslide win in the House probably wouldn’t result in a Democratic majority in 26 delegations.

No Labels denies that it’s trying to sow the seeds of a contingent election, with Mr. Clancy calling the notion a “conspiracy theorist’s fever dream” and saying that “we are getting on the 2024 presidential ballot to win the election outright in the Electoral College.”

“We will announce our selection process in early November,” Mr. Clancy said. “We are listening to America’s commonsense majority, and they — not conspiracy theorists — will choose the next president of the United States.”

Questions of a contingent election aside, there are other reasons to be skeptical of No Labels’s claim that it can win in five states. General election polls, for one, are rarely reliable more than a year out from the election.

In general, voters’ appetites for third-party candidates tend to diminish as the election draws closer and the stakes of the election become more apparent. If this doesn’t happen as the election draws nearer, expect more alarm-ringing from both major parties.

A former Harris X pollster, Adam Carlson, has also called into question the group’s opaque polling methodology, as have other critics like the Lincoln Project’s Rick Wilson, who says the group is “cooking the numbers.”

Connections between No Labels and groups aligned with Mr. Trump have also raised eyebrows over the past few months. In August, a financial backer of Mr. Trump assumed the leadership of No Labels’s Florida chapter.

A group closely associated with No Labels, the House Problem Solvers Caucus, also backed Mr. Trump’s hand picked candidate for speaker, Congressman Jim Jordan, who was apparently too conservative for House Republicans to get behind.