If this weekend was anything to go by, Pete Buttigieg might be the hottest ticket in the Democratic party right now.

The 37-year-old mayor of South Bend, Indiana, held rallies in New Hampshire on Friday and Saturday and amid talk of job growth, healthcare and military service one thing was clear: if you want to see Buttigieg, get there early.

On Friday night Buttigieg – his campaign T-shirts bear the phonetic spelling “Boot-edge-edge” – had been due to hold a rally at a brewery in Manchester. Because of demand, he switched venues at the last minute to the Currier Museum of Art. That quickly sold out too, leaving 200 people standing outside at 7.30pm.

They got to see their man. Buttigieg emerged in the drizzle, to lusty chants of “Pete! Pete! Pete!” He’d even prepared a joke.

“I hear the way you ingratiate yourself to voters is to stand on things,” he said as he clambered on to a bench. It was a reference to the folksy, table-hopping style of his Texan rival Beto O’Rourke. As a gag it would have been more impressive if Buttigieg hadn’t repeated it inside the museum 10 minutes later and at a bookstore the next day.

Buttigieg’s stump speech is not filled with jokes. Short and slight with neat hair and a slightly reedy voice, he speaks earnestly, beginning by rattling off his extremely impressive résumé.

The mayor of a city of 100,000 in the midwest, an area where Donald Trump made his biggest inroads in 2016, Buttigieg is a former navy reserve officer who served seven months in Afghanistan in 2014. He is also a Rhodes scholar who earned a first-class degree in philosophy, politics and economics from Oxford and graduated magna cum laude from Harvard.

“He seems too good to be true,” Marc Brown, who runs a T-shirt printing business in Salem, told the Guardian on Saturday. “But I like everything I’ve seen so far.”

There’s plenty to like. Buttigieg has a polished speech and a tidy way of tying his credentials to broader themes.

He talks about how the supreme court ruling in favor of same-sex marriage meant his husband could attend his mother’s bedside when she got cancer. He links his mother’s illness to the importance of universal healthcare, which then segues into the importance of reproductive health – an issue which got a huge cheer in Manchester. When Buttigieg talks about national security, he mentions his military career but also the threat of climate change and white nationalism.

“I like that he’s a veteran,” said Rebecca Small, a physician from Chester, a 20-minute drive east from Manchester. “He’s tough, but he’s smart; he speaks multiple languages, he’s very well-spoken, he’s calm. He can be fairly progressive but he knows when to dial it back.

“I’m quite liberal, but we need someone who’s kind of moderate, because we need someone to bring both sides together.”

Small, 49, echoed the sentiments of others at both Buttigieg’s New Hampshire rallies. This was a centrist, older crowd. Small is a fan of Senator Kamala Harris, from California, and former vice-president Joe Biden. Most of the people the Guardian met backed Hillary Clinton over Bernie Sanders in 2016.

“It’s interesting,” said Laurie Brown, who is married to Marc Brown, the man who seemed minorly suspicious of Buttigieg’s sparkling résumé. “It seems the younger the candidate, the older the crowd.”

Buttigieg hasn’t officially declared his White House run yet but an appearance at a CNN town hall in early March has been credited with fuelling his rapid rise. After an accomplished performance, he raised $600,000 in 24 hours. A few days later he announced he had received more than 65,000 individual donations, enough for a place in the first debate in June. At the end of March Buttigieg came third in a poll of likely Iowa voters – albeit a poll with a large margin of error. His husband, Chasten Buttigieg, whose very mention prompted big cheers in Manchester, has become something of a celebrity in his own right.

But as Buttigieg’s profile rises, things are likely to become more difficult. He might have that polished résumé, but included in there is his stint working for McKinsey and Company, a consulting firm recently named in a lawsuit against Purdue Pharma, the makers of the painkiller OxyContin. According to the Massachusetts attorney general, McKinsey advised Purdue Pharma on how to “turbocharge” sales of the drug, which is widely seen as having played a major role in the opioid crisis in the US.

McKinsey’s clients have also included the Saudi Arabian government and Immigration and Customs Enforcement, an agency some Democrats have promised to abolish. While Buttigieg speaks seven languages – he taught himself Norwegian after becoming enamoured with the author Erlend Loe – he will have to work on his defense of his consulting work.

“I never did anything that I couldn’t stand by. My specialty was in grocery prices, but I also worked on renewable energy,” Buttigieg said when the Guardian asked about his time at McKinsey.

“I did good work for our clients at the firm, I worked with good people. It’s certainly unfortunate some of the decisions that that firm has made, but I’ll leave it to the firm to answer for those choices, especially on things they made when I wasn’t working there.”

‘Sprinting a marathon’

Buttigieg may also struggle as people figure out where he fits in this huge Democratic field. He’s young and gay and describes himself as a progressive. But Clinton said she was progressive in 2016 and people at Buttigieg’s rallies don’t see him as a liberal firebrand. The person who won here last time was exactly that.

Bernie Sanders, the Democratic socialist senator from Vermont, won the New Hampshire primary with 60.1% of the vote to Clinton’s 37.6%, backed by a swell of engaged, digital-savvy young voters.

Sanders is running again, as are others on the left. At least this weekend, voters interested in Buttigieg, as well as being older, seemed more centrist-minded, a space also occupied by big hitters like Harris, Cory Booker and probably Joe Biden.

“[Buttigieg] is extremely articulate and very clear,” said Ricia McMahon, a former New Hampshire state representative from North Sutton. “He was really great tonight.”

Brown, 74, who said Buttigieg was “younger than my youngest son”, wasn’t ready to pledge her support yet, having already seen or met six candidates. But if Buttigieg can win the support of people like her it will give him a boost. Brown is a member of Ladies Left of Center, a group of 180 women who will organize around preferred candidates in the run-up to the February primary.

What is undeniable is that Buttigieg has made an incredible start. He is planning to use that fundraising boom to hire staff in key states – Iowa and New Hampshire vote in early February and 10 states will vote on Super Tuesday, 3 March – while retaining a “lean” operation, he said in Concord.

The main problem Buttigieg will face is that many of his rivals are still better known nationally, and some have been preparing for years.

Biden has run for president twice and spent eight years as VP. Harris, Booker, Warren, Amy Klobuchar and Kirsten Gillibrand are senators, as is Bernie Sanders, a phenomenon who seems to have retained much of his supporters’ enthusiasm. There’s also O’Rourke, formerly a congressman and a formidable campaigner, and Jay Inslee, the governor of Washington state, and John Hickenlooper, the former governor of Colorado.

Buttigieg, a keen jogger, said on Saturday the race for the nomination will be “like sprinting a marathon”.

It might be that Buttigieg is sprinting a marathon littered with obstacles, where crowd support is crucial and, most importantly, where he is up against a lot of sharp-elbowed competitors.