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Ms. Warren got the most enthusiastic response of the 19 candidates who appeared Saturday. Bernie Sanders, Pete Buttigieg and Cory Booker also attracted particularly energetic support.

Supporters of Democratic presidential hopefuls on Saturday at the New Hampshire Democratic Party State Convention, in Manchester, N.H.CreditElizabeth Frantz for The New York Times

MANCHESTER, N.H. — Joseph R. Biden Jr.’s backers roared supportive slogans and banged on drums as they awaited his arrival outside Southern New Hampshire University Arena. Senator Bernie Sanders was welcomed by die-hard fans ready to cheer seemingly every sentence he uttered. Mayor Pete Buttigieg and Senator Cory Booker delivered one applause line after the next.

But no one was embraced at the New Hampshire Democratic Party’s state convention Saturday quite like Elizabeth Warren.

The Massachusetts senator took the stage to a standing ovation that lasted around two minutes, and the thunderous applause that frequently interrupted her speech was amplified by the inflatable noisemakers that had been distributed to the crowd. “Win with Warren!” attendees yelled.

“There is a lot at stake, and people are scared,” she said. “But we can’t choose a candidate we don’t believe in because we’re scared.”

It’s a version of a line that Ms. Warren has deployed before, though it took on new significance days before she faces off against Mr. Biden — who is running explicitly on a message of electability — for the first time on the presidential debate stage.

Ms. Warren and Mr. Biden were two of 19 candidates who assembled here for a daylong party gathering that attracted some of the state’s most committed activists, including more than 1,200 delegates. The event was an imperfect test of the New Hampshire primary electorate — indeed, there were plenty of attendees who came from out of state.

An unknown number of Warren supporters came to the event from outside New Hampshire, judging from several social media posts of Democratic backers from Massachusetts, New York, Rhode Island and elsewhere who came to the convention for her on Saturday. Out-of-state supporters for candidates including Mr. Biden and Senator Kamala Harris also attended the event, according to interviews and social media posts. Campaigns often bus in some supporters and allies for major events. It was not clear on Saturday night to what extent the different campaigns coordinated the importing of supporters. A Warren spokeswoman declined to comment.

Still, the event did offer an early window into campaign organization and enthusiasm, in a contest that is traditionally a must-win for candidates from neighboring states

This cycle, that includes Mr. Sanders of Vermont, who won New Hampshire by a wide margin in 2016, and Ms. Warren, whose ground game is often regarded as the most extensive here.

As he has nationally, Mr. Biden has led in most New Hampshire polls since entering the race — though the surveys have been relatively few, and his campaign last week sought to downplay expectations, citing the “home-field advantage” typically enjoyed by candidates from New England. Mr. Biden, who has landed endorsements from several of the most influential Democratic leaders in the state, is focused on blue-collar voters, moderates and others who believe his more centrist brand offers the most promising path to defeating President Trump, in contrast to the more progressive coalitions Ms. Warren and Mr. Sanders are working to build.

While many voters feel warmly toward Mr. Biden, some have also referenced calculations about his standing against Mr. Trump, rather than displaying outright enthusiasm for his vision for the country.

In ways overt and subtle, both of those more liberal candidates and their supporters sought to challenge the idea that Mr. Biden is the only candidate who can win a general election.

“I am not afraid,” Ms. Warren said as she called for a “grass-roots movement” to create structural change. “And for Democrats to win, you can’t be afraid either.”

Meanwhile, inside the arena, a large banner read, “Bernie beats Trump.” Outside, another banner affixed to a pro-Sanders tent read, “In poll after poll after poll … Bernie BEATS Trump.”

Mr. Sanders received frequent applause throughout his speech and his supporters — who appeared dispersed throughout the arena — greeted many of his remarks with loud whoops.

“Together, we will make Donald Trump a one-term president,” he said. “But frankly, frankly, it is not enough just to defeat Trump. We must do much, much more. We must finally create a government and an economy that works for all of us, not just the one percent.”

Mr. Biden, the former vice president, was the first of the presidential contenders to speak, and he received a polite though not raucous reception as attendees trickled into the arena.

Taking aim at Mr. Trump, he said: “We cannot and I will not let this man be re-elected.” The audience cheered, driven in part by a contingent from the International Association of Fire Fighters.

“There’s that sense of, we know who Joe is, and we trust him,” said Sylvia Larsen, the former New Hampshire Senate president. “There’s still a little bit of people still looking around to say, ‘Well, O.K., so what else is out there?’”

Mr. Biden greeted supporters on Saturday outside the New Hampshire Democratic Party State Convention.CreditElizabeth Frantz for The New York Times

Mr. Buttigieg of South Bend, Ind., was another prominent presence at the convention: He had a large cheering contingent that punctuated his address with rounds of applause. Flush with a field-leading fund-raising haul, his campaign has significantly expanded its presence in New Hampshire and has announced the opening of 12 new offices in the state.

Senator Kamala Harris of California had a visible and vocal support section, too, boosted by her fans in bright yellow T-shirts.

Ms. Harris takes a selfie with a supporter on Saturday outside the New Hampshire Democratic Party State Convention.CreditElizabeth Frantz for The New York Times

Yet Ms. Harris’s standing in the polls has slipped over the summer, and party leaders here say she does not have the same footprint in the state as some of the other contenders. Perhaps reflecting those dynamics — and a lunchtime-hour speaking slot — her reception was uneven.

“Everybody else and the pundits can ride polls; I’m not on that roller coaster,” she told reporters after her speech. “I am working hard, we are steady, I don’t get high with the polls, I don’t go low with the polls.”

Mr. Booker, too, found himself brushing off the polls, speaking to reporters after giving a well-received speech. His candidacy has mystified some veteran New Hampshire Democrats who note his relatively stagnant poll numbers despite extensive on-the-ground campaign organization, and mounting endorsements.

Given the huge cast of candidates — and how seriously New Hampshire residents take their status as the first primary voters — many voters are in no mood to commit this early. It is another reminder that the polls could change dramatically before the primary next February.

“I think of it like getting an ice cream sundae and trying to decide what toppings you want to put on your ice cream, because they’re very good choices, but I just can’t make up my mind,” said Jeanne Brown from Goffstown, N.H., who attended a Warren event in Bow, N.H., over the summer. “You know, I don’t know if I want the gummy bears or the sprinkles.”

Ms. Warren of Massachusetts dove into a crowd of her supporters.CreditElizabeth Frantz for The New York Times

That same indecision was on display Saturday.

“I have been waving signs for all the candidates, as have most people on the floor,” said State Representative Kris Schultz, a progressive leader who said that her top choices were Ms. Warren, Mr. Sanders and Mr. Booker — adding that the New Jersey senator is “amazing.” “Lots of people remain undecided.”

And for all of the enthusiasm for Ms. Warren, some attendees continued to have reservations about her ability to defeat Mr. Trump.

“Senator Warren is probably the best campaigner out there, but in order to get elected against Trump I think she’s going to have to moderate some of her priorities,” said New Hampshire State Representative David Karrick Jr.

Ahead of the event, activists and other voters rattled off lists of their top three choices, but repeatedly stressed that their rankings could shift. For at least one voter, they changed in a matter of moments.

“Pete, Warren and then Biden,” said Tim Ashe of Somersworth, N.H., referencing Mr. Buttigieg. “That may change.”

When asked why Mr. Buttigieg was his first choice, he replied, “I was looking at a Pete sign when I said it.”

“If I had to vote today,” he added, “it would probably be for Warren.”

His wife, Laurie Ashe, said that she had supported John Kasich, the former Republican governor of Ohio, in the primary in 2016 and then voted for Hillary Clinton in the general election. Now, she said, she is supporting Ms. Warren, because “regular people cannot work their way into the middle class anymore.”

Jonathan Martin contributed reporting from Bow, N.H.

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A version of this article appears in print on , Section A, Page 18 of the New York edition with the headline: At a Democratic Event in New Hampshire, Warren Stands Out. Order Reprints | Today’s Paper | Subscribe