DES MOINES — Pete Buttigieg, the 37-year-old mayor of South Bend, Ind., raised more money than any other contender in the 2020 presidential field during the last fundraising quarter. He has traveled around the country for months trying to introduce himself to Americans and given dozens of media interviews to raise his profile.

But as he made his way down the grand concourse of the Iowa State Fair not long ago, surrounded by a horde of cameras, a woman stopped dead in her tracks looking at the mob. She squinted and cocked her head, trying to identify the young man ahead of her before giving up.

“Who are you?” the woman called out, as the candidate passed by.

“My name is Pete,” Buttigieg responded. “I’m running for president.”

“Who?” she replied.

Buttigieg on Saturday began airing his first ad, in Iowa, to reintroduce himself and surmount a challenge familiar to many presidential candidates still in the race but struggling to grow their support — finding a breakthrough message that persuades people to vote for him rather than others in this year’s historically large field of candidates.

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The still-fluid race for the Democratic nomination has split into two distinct groups: the candidates who have succeeded in crafting a distinct message and those who haven’t.

For months, the three top-polling Democratic candidates have distinguished themselves with crystal-clear, if varied, arguments. Former vice president Joe Biden is running to “restore the soul” of the country to the pre-Donald Trump era. Sen. Bernie Sanders (I-Vt.) promises a Democratic-socialist revolution that puts government in charge of huge sectors of the economy. And Sen. Elizabeth Warren (D-Mass.) is asking the country to “dream big” for structural changes to take away the power of economic and political elites.

The others in the race have found it more difficult to offer the same kind of coherence between their policy and campaign approaches, and are still developing their pitch and the organization to back it up months after their announcements.

After an uneven start, former congressman Beto O’Rourke (D-Tex.) refashioned his campaign in August as a moral crusade against Trumpism, after a mass shooting in his hometown of El Paso. Sen. Kamala D. Harris (D-Calif.) has shifted her focus, casting herself more recently as “a problem-solving president,” and a foil to both the more sweeping, ideological government overhauls advocated by Sanders and Warren and the return to normalcy advertised by Biden. But that pitch requires far more explanation than the alternatives.

Buttigieg is facing pressure to demonstrate that he has the message that can elevate his campaign to match the hype and expectations he fanned early on in some corners of the party.

Privately, Democrats close to the campaign have urged Buttigieg to offer a more clarifying argument for why he’s running for president and why his candidacy is distinctive.

“You have got to have a reason for why people will vote for you. And it has got to be easily articulatable. It has got to be ‘here’s what I stand for,’ not what I am not for,” said a Democrat close to the Buttigieg campaign who spoke on the condition of anonymity to candidly discuss the mayor’s strategy.

Buttigieg seems to be trying. In his Iowa ad, which features an image of Buttigieg during his 2014 tour of duty in Afghanistan with the Navy Reserve, he presents himself as a calm, fresh-faced outsider from Washington offering “real solutions, not more polarization.”

He has echoed that message on the trail in recent weeks, refining his vague “Win the Era” slogan to an argument meant to more firmly position him as a next-generation change agent, with center-left policy views like Biden and an urgency to shake up the system more reminiscent of Warren and Sanders, the liberal disrupters in the race.

“I’m afraid our country is running out of time,” Buttigieg recently told a group of 500 voters in Fairfield, Iowa. “If we are going to move our country forward, it’s going to require walking away from that recycled set of arguments that hasn’t gotten us anywhere and actually getting something done. That’s why I am running for president.”

As Buttigieg tweaks his message, his campaign has launched a surge of staff and resources in first-voting Iowa. As of this past week, Buttigieg had 100 staffers on the ground, the largest organization in the state, competing with Warren, Harris and others who have had substantial operations for months. The campaign is opening 20 district offices and plans to hire more staff in coming weeks. He also is expanding in the first primary state, New Hampshire.

Even some of Buttigieg’s biggest supporters admit that time is short to grow his support beyond the 5 to 8 percent he has received in polls, both nationally and in Iowa and New Hampshire.

“They are putting it together, but the jury is still out on whether they put it together fast enough,” said the Democrat close to the campaign. “This is a critical moment. Either he starts moving up in the polls soon or he will be in trouble.”

Buttigieg’s campaign insists it will capi­tal­ize on greater attention from voters now that summer has passed, by increasing outreach and visits to the state. The campaign is hoping to boost momentum with a big turnout of supporters at the upcoming Polk County Democrats Steak Fry — a celebrated Iowa event that propelled Barack Obama into serious presidential contention ahead of the 2008 caucuses.

“It’s going to be a little like turning on a light switch,” said Jess O’Connell, a longtime Democratic strategist and former chief executive of the Democratic National Committee who joined the Buttigieg campaign in July as a senior adviser overseeing early-state strategy.

Some local county chairs and Democratic activists in Iowa have grumbled they haven’t heard enough from the Buttigieg campaign. Yet on a recent campaign swing through Iowa, before his staff surge, Buttigieg attracted crowds equal to or larger than those who recently turned out for leading candidates — and larger than other candidates stuck in single digits.

In Burlington, Iowa, about 500 people turned out to see Buttigieg on a recent Tuesday evening — compared with 250 who had turned out for Biden and about 300 for Harris just days before. Another 225 people squeezed into a ballroom at the Hotel Ottumwa in Ottumwa, a popular destination for Democratic hopefuls lately where Warren attracted about the same sized crowd during a visit in May.

In Tipton, where Buttigieg unveiled a policy to boost rural America to a crowd of exactly 302, Bob and Linda Ofner from Davenport, Iowa, raved about the mayor’s appearance, saying they had been “all in” for his campaign for months after seeing him speak on television.

But they worried that Buttigieg had been too slow to open offices around the state, including in Davenport, and hadn’t had a presence at a recent county fair or other local events. They worried his slow ramp-up had robbed him of hiring in-state talent; most of the staffers they knew were from out of state and unfamiliar with local voters.

“The thing that gives me hope is that Obama was behind Hillary [Clinton] at this point, and then he kicked butt,” Linda Ofner said. “They are hiring like crazy, but they just need to get out there and get him out there in front of more people.”

Aware its candidate is lagging, the Buttigieg campaign has launched an aggressive organizing strategy cultivating what aides described as “super committed” voters by tapping the personal networks of supporters — a move modeled in part after Obama’s successful organizing effort in 2008.

But he is playing catch-up to rivals like Warren, who has had staffers deeply embedded in many communities for months in an attempt to forge their own personal connections.

In a recent swing through Iowa, Buttigieg appeared to be trying to target Democrats who had been attracted to Trump’s message in 2016. He traveled through southeastern Iowa, visiting counties that had voted for Obama and then for Trump, where voters tend to be more conservative and deeply religious. In his remarks, Buttigieg repeatedly emphasized his religious values, speaking at length about his faith and arguing that “God does not belong to a political party.”

At the same time, Buttigieg rarely mentioned what would be the most radical aspect of his presidency: If elected, he would be the nation’s first gay president.

“Whenever I enthuse about you to a friend or an acquaintance, they say, yeah I agree, but America isn’t ready to elect a gay man as president,” a man told Buttigieg in Fairfield, asking the mayor how he should encourage people to “take a risk.”

Buttigieg replied by telling the story of his decision to come out as mayor of South Bend, a city that is “socially conservative,” but later reelected him with 80 percent of the vote. He then changed the subject.

“I might add, in going up against this president, it would be useful to have a voice from the middle of the country,” he said to cheers.

It was one of the tightest messages he offered.