GRINNELL, Iowa — When news first spread that a young, openly gay mayor from Indiana was running for president, the liberal potential of his candidacy seemed limitless: Pete Buttigieg supported Medicare-for-all, preached urgency on climate change, and demanded reforms such as abolishing the electoral college and overhauling the Supreme Court.

Eleven months later, Buttigieg looks more like a traditional centrist than a leftist force. Instead of Medicare-for-all, he favors a more limited public option. Environmentalists complain his climate plan is less sweeping than his early rhetoric suggested it might be. After raising his hand at a debate to show support for decriminalizing border crossings, he clarified that he doesn’t actually hold that position.

The shifts reflect in part the broader trajectory of the Democratic primary, which initially appeared to herald a dramatic leftward surge. The center of gravity is settling in a less revolutionary place. Many liberals — at first excited by Buttigieg and the change he promised — now see him as embodying a dynamic they find deeply frustrating.

The evolution is arguably working for Buttigieg, who regularly polls in the top tier of the Democratic candidates. But it has also given rise to complaints that the mayor of South Bend, Ind., is carefully calculating his positions rather than passionately expressing his principles.

The tension has begun flaring up regularly on the campaign trail. Some of Buttigieg’s former supporters are even using Twitter to ask for their donations back, deploying the hashtag #RefundPete.

At a recent campaign event at Iowa’s Grinnell College, when Buttigieg’s aides signaled it was time to wrap up, the candidate instead turned to a group that had been holding signs in the front row and asked resignedly, “Do you want to do the thing?”

They stood and held up sheets with protest messages, which Buttigieg read off one by one before responding. “Wall Street Pete” said one; Buttigieg shot back, “They said the same thing about Obama.” Another said “You will kill us;” Buttigieg answered, “That’s mean. I’m here to help.”

Buttigieg is not alone among the Democrats in scooting toward the center. While Sen. Bernie Sanders (I-Vt.) has maintained his left-leaning positions — and even amplified them — much of the rest of the field has slid away from him.

Sen. Elizabeth Warren (D-Mass.), while still a forceful liberal, has backed away from her unconditional support for Medicare-for-all. Sen. Kamala D. Harris (D-Calif.), before dropping out, moved from campaigning as an outspoken liberal to touting more centrist credentials. Former vice president Joe Biden, a centrist who many thought would struggle, has instead maintained a strong position in the polls.

But it is Buttigieg who is prompting the most “animosity,” said Jonathan Westin, executive director of New York Communities for Change, adding that his members are “completely offended” by how the mayor is campaigning.

“I think it just gets down to a lot of the doublespeak Mayor Pete has been doing throughout the campaign,” Westin said. “Saying he is for Medicare-for-all, then walking back, changing his position on issues, claiming to be the millennial change candidate while at the same time cozying up to billionaire donors. He’s running a really insider campaign, and it speaks to how he would govern if he were elected.”

Buttigieg’s campaign brushes off such complaints as “noise,” coming from people whose views do not represent the broader electorate.

“We’re not focused on the small echo chamber of Washington insiders talking to each other on Twitter,” said Buttigieg spokesman Chris Meagher. “We’re focused on talking to voters about the issues that matter most to voters.”

Buttigieg himself called the vocal opposition he has encountered “a little strange,” telling The Washington Post’s Robert Costa in a recent interview, “I think that I broadly share the same values and goals as a lot of these folks. It’s a little hard to have a conversation with them, so, I don’t know for sure.”

He added, “Part of our democratic process, in all of its messy beauty, is that individuals can choose whether they’re going to focus on supporting a candidate they believe in, or coming to something you’re doing and holding up a sign or chanting.”

The liberal frustration, however, comes partly from a sense that Buttigieg espoused more progressive positions as he launched his campaign but abandoned them when it became expedient, as he transformed from boundary breaker to actual contender.

How much he has moved depends on where people saw him in the first place. Early on, Buttigieg rolled out few policy specifics, instead signaling a generally activist approach by urging reform of the Supreme Court and the electoral college.

In part, that was practical: While some of his opponents boasted seasoned campaign operations growing out of long political careers, Buttigieg, the mayor of a medium-sized city, started with a bare-bones operation. But the unknowns allowed voters to project their own perceptions onto him.

What many of those voters saw was an eloquent 37-year-old, a thoughtful mayor and veteran who would be the youngest person ever to serve as president. Others saw a proudly married gay man who could help turn the page on a long-standing prejudice.

It was only later in the year that Buttigieg filled in the blanks with more detailed policy proposals. His first major speech on the economy did not come until late July. His plan to address gun violence followed in early August. He outlined details of his health plan in mid-September, months after some of his rivals.

As the plans fleshed out, they often showed a centrist tilt. Buttigieg’s climate plan, for example, envisions up to $2 trillion in investment, compared to $16 trillion for Sanders — though Buttigieg regularly says that the effectiveness of a plan should not be measured in its costliness.

The Sunrise Movement, a climate group, which had praised Buttigieg’s rhetoric on a Green New Deal in March, staged a sit-in at his South Bend office in November, saying his climate plan for the city demonstrated too little urgency. The group has also protested his national plan.

Even Buttigieg’s handling of his sexuality has become a source of frustration for those disappointed he has not spoken out more forcefully on LGBT rights. Brian Gaither, co-founder of Maryland LGBT PAC, donated to Buttigieg at the beginning of his campaign, but he has now asked for a refund and added #NeverPete to his Twitter profile.

Gaither said he feels “conned,” adding that he wished Buttigieg spoke more clearly about his sexuality — the most groundbreaking aspect of his candidacy — instead of making relatively vague references to his “marriage” or “marrying a teacher.”

“It’s not that he has to be obligated to be activist of the year, but there seems to be a very specific distancing of himself from any obligation to be concerned or know about those things,” Gaither said. “It’s really hard to understand where he wants to be, other than to use the opportunity to be the first openly gay candidate as a way for his campaign to have significance and meaning it otherwise would not have.”

Federal Election Commission reports show Buttigieg has spent three times as much on polling as any other candidate in the field, much of it conducted by the Benenson Strategy Group, which also polled for Barack Obama and Hillary Clinton.

The group began conducting focus groups for Buttigieg last summer, and many of his big policy initiatives — a “Douglass plan” on racial justice, a proposed public option on health care — arrived after that polling began. That timeline has fed into the liberal complaints that Buttigieg is a political weather vane.

His shift on health care — not unique in this field — is particularly clear. In 2018, Buttigieg tweeted his full support for Medicare-for-all. Throughout 2019, the campaign told The Post, which is tracking the candidates’ positions, that he was supporting “some version of Medicare-for-all.” But earlier this month, aides said that should be changed to “prefers a public option.”

Buttigieg’s backers say such adjustments do not amount to flip-flopping, but rather to defining with more nuance how best to accomplish broadly liberal goals. They also say that if elected, Buttigieg would still be the most liberal president in decades.

“To the extent that he has veered at all, I would ascribe it more to a combination of the inherent nature of a campaign and they have become more sophisticated in defining the campaign,” said one supporter close to Buttigieg’s senior staff, who requested anonymity to speak more freely. “Any candidate who has a chance to win does that.”

The Buttigieg campaign has also responded to some of the critiques, especially those voiced by Warren, with whom he is locked in a fierce battle for white, college-educated voters that make up a large portion of their shared base. After she criticized him for not being transparent, Buttigieg opened his fundraisers to reporters and disclosed a list of his clients when he worked as a consultant after college.

But if Buttigieg has altered some messaging, his policy substance now places him squarely in the centrist faction of the Democratic field. That puts him in the same camp as Biden, and it distances him from Warren and Sanders.

It also means Buttigieg has in effect taken sides in the big debate dividing the Democratic Party — whether to focus on energizing the liberal base or reaching out to the center.

Some centrists think he has made the right call.

“I think you just have to hold the line,” said Rep. Tim Ryan (D-Ohio), who ended his own presidential campaign in October. “We can’t get thrown off with some of these positions that aren’t going to play well in the states we need to win. Decriminalizing at the border, free health care for undocumented workers — all of those are positions that make it very, very difficult to win in these states.”

Kevin M. Uhrmacher contributed to this report.