MANCHESTER, N.H. — It took until midafternoon here for Democrats in the first-in-the-nation primary state to start showing some real enthusiasm for their presidential candidates who traveled here for the party convention.

When Sen. Bernie Sanders (I-Vt.) took the stage Saturday, a huge roar came from the left bleachers, where his supporters had packed the stadium seats at the SNHU Arena. And later, when the name of Sen. Elizabeth Warren (D-Mass.) was announced, the entire area erupted, with thousands banging together inflatable “thunder sticks” emblazoned with the slogan: “Win With Warren.”

“If people are looking for a safe harbor, it’s Joe Biden. If they’re looking for change — which really won’t be much quieter than what we have now — then it’s Elizabeth Warren,” said Howard Cunningham, a New Hampshire delegate. “It depends what you want out of your government in terms of the near future.”

While Sanders and Warren, who are the most liberal in the field, don’t lead in early polls, the overwhelming response suggested some blend of superior organization from the campaigns and untapped excitement from the most plugged-in voters and party activists who attended Saturday’s event. It also doesn’t hurt that both are from states that border New Hampshire.

Both are potent forces who are likely to continue to matter as the massive Democratic field narrows over the next few months.

Warren, who has struggled with a notion in the minds of many voters that she won’t be able to beat President Trump, tried to harness the affection that voters are showering on her and use that as an argument that she should lead the party.

“We need to win in 2020. Anybody in here want to win in 2020?” Warren asked. “I get it, there is a lot at stake and people are scared. But we can’t choose a candidate we don’t believe in because we’re scared.”

Sanders also made case that he can win. “We are beating Donald Trump in every poll that’s ever been done,” Sanders said to supporters gathered to see him at a bar across the street from the convention center. “The last poll, I believe, had us up by 12 points.” It was a reference to a recent national poll by Quinnipiac University, which also found Biden and Warren leading Trump by double digits.

Biden, the former vice president, was the first presidential candidate to address the convention, and he hit many of the same themes that he’s talked about before in his campaign.

“Folks, Wall Street did not build this country. You built this country,” Biden said, offering a riff similar to one that Warren first gave during her 2012 Senate campaign.

Biden made an emotional appeal to stand up to a president he feels is “more similar to George Wallace than George Washington.”

Biden’s speech was met with polite applause, but his supporters said it’s a mistake to read too much into crowd reaction.

“I’ll tell you what, I’d much rather have Joe, who maybe makes a misstatement now and then than a president who lied to the American people virtually every day,” said Harold A. Schaitberger, who leads the International Association of Firefighters and came with a large contingent of union members to cheer for Biden.

He downplayed the outward shows of enthusiasm for other candidates: “The voting population within the Democratic Party, I believe, resides in the lane that Joe Biden commands.”

But in a reminder of why some Democrats are concerned, Biden drew chuckles from the crowd when he misstated the president’s name during his speech here.

“If Donald Hump — if Donald Trump is reelected, Freudian slip, if Donald Trump is reelected he will forever and fundamentally alter the character of this nation,” Biden said.

Biden’s verbal miscues prompted one competitor, Rep. Tim Ryan (D-Ohio), to question the former vice president’s fitness for office.

In an interview published by Bloomberg News, Ryan said he believes Biden is “declining.” On Saturday, when pressed by reporters, Ryan said: “I’m just saying that it’s unclear sometimes when he is articulating positions. There’s a lack of clarity, and I’ll leave it at that.”

Kate Bedingfield, a spokeswoman with Biden’s campaign, declined to comment on Ryan’s remarks.

Many of the candidates with lower-tier polling numbers moved into more of a pundit role about their own campaigns.

When asked by a reporter about his lagging poll numbers, Sen. Cory Booker (D-N.J.) said “thank God” he’s low in the polls.

“We’ve never had a candidate who is ahead of the polls this far out who’s ever gone on to be president,” Booker said, adding that former presidents Bill Clinton and Barack Obama were “long shots” at this point in the race.

Former Obama administration housing secretary Julián Castro said he believes his campaign will pick up.

“We’re entering a new phase in the campaign with these September and October debates as people look at these 10 candidates,” Castro said. “I believe they’re going to try to figure out who can reassemble that Obama coalition.”

Sen. Kamala D. Harris (D-Calif.) has been forced to play pundit more than she might prefer lately, as reporters begin to ask about her stagnant polling numbers more and more — at almost every one of her public appearances in the past two weeks.

On Saturday, she answered again.

“The issue of polls to me, depending on the polls, sample size, the day of the week — I’m not riding polls,” Harris said. “I don’t ride on that roller coaster. I’m working hard. We are steady. I don’t get high with the polls, I don’t get low with the polls.”

Cleve R. Wootson Jr. and David Weigel contributed to this report.