No Labels, the group that for months has pledged to run a centrist presidential ticket in the event of a rematch between President Biden and former President Donald J. Trump, is running out of time to recruit a standard-bearer after a string of rejections.
With a number of prominent prospective candidates saying no thanks in recent months, some No Labels members and leaders have grown frustrated with the failure to advance a ticket, according to two people involved with the group and notes provided to The New York Times from a recent video meeting of No Labels delegates.
Still, the group’s leadership continues to hold out hope for November, even as the possibility of outright defeating both Mr. Biden and Mr. Trump seems increasingly remote. Leaders have promoted a far-fetched scenario in which the group could play the role of power broker in the general election if neither major-party candidate reaches an outright majority.
As the group charts a path forward, deadlines to get on state ballots are approaching.
“To be credible, you want to be on the ballot in every state,” former Representative Tom Davis of Virginia, a No Labels co-founder, said in an interview.
“Although,” he added, “you know, Lincoln wasn’t on the ballot in 10 states, and he won.”
For putting together a ticket, Mr. Davis said, “April 15 is kind of their drop-dead date.” The April 15 deadline matters because independent candidates for president can begin collecting signatures after that to qualify for the ballot in New York State.
“If you want to be on the ballot in New York, that’s what drives it,” he added.
No Labels is currently on the ballot in 18 states, the group says. Last year, it said it had already raised $60 million to put forward what it called a “unity ticket,” with one Democrat and one Republican. By the fall, the group’s president, Nancy Jacobson, told potential donors and allies that she had committed to choosing a Republican as the No Labels presidential candidate. No such person has emerged.
Mr. Davis was among the participants in a video conference for some of the group’s delegates and leaders on Tuesday, in which Ms. Jacobson said several top choices for the group’s ticket were not interested, according to two people who participated in the call.
Those names included retired Adm. William H. McRaven, former Secretary of State Condoleezza Rice and former Representative Will Hurd of Texas. Another prospective recruit, former Lt. Gov. Geoff Duncan of Georgia, a Republican, had publicly withdrawn his name from consideration on Monday.
Ms. Jacobson told the delegates on the video conference that she had not given up, but that the group’s leaders did not know if they could find a “gladiator” who was willing to take on the role, according to one of the people who participated in the meeting.
Ms. Jacobson and a spokeswoman for No Labels did not respond to calls, text messages or emails.
Several delegates on the video conference expressed disappointment and frustration that no candidate had taken up the opportunity to head the ticket. Some threw out additional names for the group to consider: Robert F. Kennedy Jr., the independent presidential candidate; Nikki Haley, the former Republican presidential candidate; and David H. Petraeus, the retired general and former C.I.A. director.
Mr. Kennedy did not respond to a request for comment. Ms. Haley, who bowed out of the G.O.P. race earlier this month, has already ruled out a No Labels bid because, she said, she would not accept a Democratic running mate.
General Petraeus said on Thursday that he had been approached and had said no.
Admiral McRaven, Mr. Hurd and Ms. Rice did not immediately return requests for comment.
Later in Tuesday’s video conference, Mr. Davis walked the group through a scenario in which a No Labels ticket could win several states in the general election, depriving Mr. Biden and Mr. Trump of the 270 electoral college votes required to win.
Such an outcome would prompt a contingent election — a constitutional provision by which the president is chosen by the House of Representatives, and the vice president by the Senate. Such a scenario has not occurred since the 1800s.
In Mr. Davis’s telling, representatives of a major party might opt for the No Labels candidate over the other party’s candidate. In the interview, Mr. Davis said he had discussed the matter on the call to address concerns among delegates about the possibility. He also said Mr. Biden was inviting such a scenario by, in Mr. Davis’s view, framing his campaign as an effort purely to stop Mr. Trump.
“It seems to me Biden is more interested in stopping Trump than anything else,” Mr. Davis said. “Funny things happen. That’s all I can say.”
A contingent election would be a “mind-boggling disaster,” said William Ewald, a constitutional legal scholar at Carey Law School at the University of Pennsylvania. “In an election in the present political climate, whoever won, there would be people rioting in the streets, and not figuratively.”
On Tuesday’s video conference, Mr. Davis — once a fixture of the moderate Republican establishment that has been exiled by the forces aligned behind Mr. Trump — described how No Labels might intervene before the matter even made it to Congress.
In his scenario, so-called faithless electors from any number of states might trade their support for “policy concessions” brokered by No Labels.
On the videoconference and again during the interview, Mr. Davis cited the election of 1876 and its aftermath as an example of how this year’s election could go if neither of the major-party candidates accumulates 270 electoral votes, or if electors refuse to support the candidates in the Electoral College.
In that election, after no outright winner emerged, an electoral commission ultimately awarded contested votes to Rutherford B. Hayes, a Republican, in an arrangement made possible by the Compromise of 1877, in which Republicans agreed to withdraw federal troops from Southern states, ending Reconstruction.
Third Way, a Democratic group that has repeatedly raised concerns about No Labels, called the group’s flirtation with such a plan a grave threat to democracy.
“It’s impossible to overstate how chaotic and dangerous it would be for a party in this election to intentionally try to cause a contingent election that would result in enormous confusion and perhaps political violence,” said Matt Bennett, a co-founder of Third Way.
As recently as January, No Labels was still courting or considering prominent current and former politicians, including Bill Haslam, a Republican and a former governor of Tennessee; Jon Huntsman, a Republican and a former governor of Utah; Larry Hogan, a Republican and a former governor of Maryland; and Senator Joe Manchin III, the conservative West Virginia Democrat who is not seeking re-election.
Mr. Haslam never considered entertaining No Labels’s invitation, according to a person briefed on the discussion.In February, Mr. Hogan announced a plan to run for Maryland’s open Senate seat. A week later, Mr. Manchin ruled out running for president.