If President Biden’s re-election campaign can feel like a slog elsewhere, the write-in effort for him in New Hampshire’s primary election is infused with the sort of joy found in spirited underdogs.

Veteran Democrats in the state have been pushing the party’s voters and independents to write in the name of Mr. Biden on Tuesday, a move necessitated by his absence from the ballot after New Hampshire fought his decision to push the state back on the nominating calendar.

The effort has energized New Hampshire Democrats, who have long chafed under the micromanagement of national party leaders. The write-in effort has freed them from outside interference and allowed them to run a campaign as they like.

And they are growing optimistic.

With no backing or communication from the Democratic National Committee or Mr. Biden’s campaign headquarters in Delaware, these New Hampshire Democrats, who began the Write-In Biden campaign late last year, now expect to help deliver the president an overwhelming victory.

“There’s a lot going on here to support Joe Biden,” said Kathleen Sullivan, a former chairwoman of the New Hampshire Democratic Party who is leading a write-in Biden super PAC. “We’ve been able to build some energy and excitement and support for him that we’re not seeing anywhere else in the country.”

Mr. Biden did not submit his name for the primary ballot after New Hampshire refused to comply with the Democratic National Committee’s new calendar, which made South Carolina the first presidential nominating state.

Other Democrats running challenges to Mr. Biden are trying to capitalize — including Representative Dean Phillips of Minnesota, the author Marianne Williamson and 19 other Democrats on New Hampshire’s expansive primary ballot.

Mr. Biden’s campaign declined to comment on the state’s primary election. In an interview on Friday in Seneca, S.C., Jaime Harrison, the D.N.C. chairman, dismissed New Hampshire’s contest as irrelevant and pleaded ignorance about the write-in Biden effort.

“Our first-in-the-nation primary is here in South Carolina, and that’s what I’m focused on,” Mr. Harrison said. “So I’m not sure or aware what they’re doing in New Hampshire.”

While the formal Democratic Party apparatus has stayed away from New Hampshire and the state hasn’t had a presidential visit since 2022, the Biden administration has curiously still showered the state with attention.

New Hampshire Public Radio noted that in one week this month, five secretaries in Mr. Biden’s cabinet visited the state — though none would speak directly about the primary race.

Mr. Phillips has spent millions of dollars on television ads in New Hampshire, and Ms. Williamson has activated supporters who were involved in her 2020 campaign — when she placed 14th with 95 votes. A poll released Sunday from CNN and the University of New Hampshire showed that 63 percent of likely voters in the state’s Democratic primary said they would write in Mr. Biden, 10 percent planned to vote for Mr. Phillips and 9 percent were set to back Ms. Williamson.

In the primary’s final days, New Hampshire Democrats who are supporting Mr. Biden engaged in a bit of self-congratulation while dismissing Mr. Phillips as a nonentity.

Representative Ann McLane Kuster, a Democrat who represents the western and northern parts of the state, said a commanding write-in triumph for Mr. Biden would send a signal that he had no legitimate Democratic challengers. She said Mr. Phillips could place behind Ms. Williamson.

“Imagine if we hadn’t done the write-in and nobody voted,” she said over lunch on Saturday in Manchester. “Then the story would have been, oh, Donald Trump is in, but we don’t know who it’s going to be on our side.”

Mr. Phillips, who began his campaign in October, just before the deadline to qualify for the New Hampshire ballot, said he would deliver “a real surprise” in the state but stopped far short of promising a victory over a candidate who isn’t on the ballot.

“As for Tuesday night, I think anything’s going to be a success,” he told reporters after a campaign stop on Saturday in Nashua. “If I’m in double digits or in the 20s, is what I’d like to see. Either way, I’m going to keep going.”

Mr. Phillips said he would take his campaign to Michigan next, and then to South Carolina. He said he could not name a state where he believed he would win a primary against Mr. Biden, whom he characterized as weak and likely to lose the general election.

“If he is somewhere in the 50s or 60s, I think that is the demonstration of both his weakness and unelectability,” Mr. Phillips said. “The country will have to note that and Democrats will have to finally wake up from their delusion about him.

There is also a low-budget campaign to encourage New Hampshire Democrats who are angry at Mr. Biden’s stance on the Israel-Gaza war to write in “cease-fire.”

William Shaheen, a longtime New Hampshire Democratic activist who is married to the state’s senior senator, Jeanne Shaheen, said that despite the write-in effort’s visibility in direct mail and in the local news media, it was still very uncertain how many people would go to the polls to back Mr. Biden.

Independent voters, he said, will be far more likely to vote in the Republican primary for what may be a final opportunity to block Mr. Trump.

“If New Hampshire was officially the first-in-the-nation primary by the D.N.C., I think it would be a blowout in Joe Biden’s favor,” Mr. Shaheen said. “It makes it a little more difficult to go out and write his name in.”

He added, “I don’t think a lot of people who are independents are going to go and write in Joe Biden’s name.”

Ms. Sullivan called the local write-in effort for Mr. Biden “liberating and refreshing” after decades of working for presidential campaigns with orders being sent from faraway states.

“If you had a group of people from New Hampshire two days before the primary, we’d be complaining about the people running the campaign,” she said. “We’re not doing that because it’s being run by grass-roots folks.”

She said the Biden campaign would be wise to turn to New Hampshire Democrats for advice on how to run its general-election campaign in the state.

“We’ll be happy to tell them what we think they should be doing,” Ms. Sullivan said.

Maya King contributed reporting from Seneca, S.C.

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