Now that the centrist third-party group No Labels is abandoning its effort to field a presidential “unity ticket” in 2024, Democrats and anti-Trump Republicans are turning their focus to cutting off the other third-party challenger — Robert F. Kennedy Jr.

No Labels announced Thursday that it would not run a presidential ticket this cycle. That comes after the group failed to find a high-profile candidate willing to run on the line. The announcement comes one week after the group’s founding chairman, Senator Lieberman, died after a fall.

“Americans remain more open to an independent presidential run, and hungrier for unifying national leadership, than ever before,” No Labels says. “But No Labels has always said we would only offer our ballot line to a ticket if we could identify candidates with a credible path to winning the White House. No such candidates emerged, so the responsible course of action is to stand down.”

Biden supporters are celebrating. While No Labels billed itself as representing the “commonsense middle” and vowed to run a “unity ticket” with a Republican and Democrat or Independent in the vice-presidential slot, Democrats feared it would pull more votes from President Biden than President Trump.

Governor Christie announced last week that he was declining to run with No Labels after polling showed no path to victory for him. “If there is not a pathway to win and if my candidacy in any way, shape or form would help Donald Trump become president again, then it is not the way forward,” he posted to X.

Governor Haley and the lieutenant governor of Georgia, Geoff Duncan, also declined to run with No Labels. A moderate Democratic senator, Joe Manchin, and moderate Republican governor, Larry Hogan, said “no” to No Labels earlier this year and have distanced themselves from the group.

With No Labels out, Democratic operatives are turning their focus to Mr. Kennedy. In picking for his running mate tech entrepreneur Nicole Shanahan, a former Democratic donor, Mr. Kennedy likely represents a bigger threat to Mr. Biden than Mr. Trump. 

Former Republican and Lincoln Project co-founder Rick Wilson released a video to X Thursday celebrating No Labels’ “decline and fall.” He called the group’s effort a “quixotic pro-Trump presidential plan” and a “gigantic waste of $70 million of Republican donor money.”

“We are delighted that No Labels is off the radar screen for 2024. This is a net positive for Joe Biden,” Mr. Wilson says. “Over to you now Robert F. Kennedy Jr. You’re next on the list of spoilers who need to be addressed politically in a way you’re not accustomed to being addressed yet.”

The Democratic National Committee has reportedly set up a whole unit to deal with third-party challengers. This comes after the party failed to take Green Party challenger Jill Stein seriously in 2016, possibly costing Hillary Clinton the election. Ms. Stein is running again this year.

“Now it’s time for Robert Kennedy Jr. to see the writing on the wall that no third-party challenger has a path forward to winning the presidency,” the executive director of MoveOn, Rahna Epting, said Thursday.

 Mr. Kennedy this week called Mr. Biden a “much worse threat to democracy” than Mr. Trump. He likes to point out the hypocrisy of the Democratic Party running on a pro-democracy platform while trying to limit voters’ choices.

“The failure of No Labels to get ballot access and field a candidate is testimony to the stranglehold of the corrupt two-party duopoly on American democracy,” Mr. Kennedy’s campaign press secretary, Stephanie Spear, tells the Sun by email. “The success of the Kennedy campaign shows Americans are ready for a third choice. This is the election where the lesser-of-two-evils voting ends.”

Mr. Kennedy is mounting the most formidable independent presidential challenge since Ross Perot in 1992. He is polling on average at 12 percent. His campaign has achieved ballot access in only one state, but it says it has already gotten enough signatures to be on the ballot in five more and expects to be on in all 50 states. 

The Democratic National Committee wants to make 2024 a two-person race — the formula that facilitated Mr. Biden’s 2020 victory. This means the attacks on Mr. Kennedy will only ramp up.

After Mr. Kennedy’s vice-presidential announcement in Oakland last week, the Democratic National Committee held a response Zoom call for reporters. In it, they called Mr. Kennedy a “tinfoil hat conspiracy theorist” who is trading on his family name and painted him as a spoiler for Mr. Trump.

“We cannot afford Donald Trump to be back in the White House, which is what is going to happen if people don’t see RFK for what he actually is, which is Donald Trump with a Kennedy name slapped on him,” a Democratic state senator from Michigan, Mallory McMorrow, said.