MASON CITY, Iowa — The stars are starting to align for Pete Buttigieg here in Iowa, where his rivals’ struggles and far-left aspirations have given the South Bend, Indiana, mayor room to run in the first-in-the-nation caucus state.

Mr. Buttigieg is so upbeat about his rise among the crowded field of Democratic presidential hopefuls that he is leaning into comparisons with former President Barack Obama — another “young man with a funny name” — and gone so far as to predict he is on a collision course with Sen. Elizabeth Warren of Massachusetts, a boast he’s since tried to walk back.

“Based on what I’m seeing here and across the state I am pretty sure you are going to make me the nominee and the next president of the United States,” Mr. Buttigieg told voters that came out to see him during a three-day bus tour of northern Iowa.

The prospect of a Buttigieg victory in Iowa seemed far-fetched when he entered the race in May, but the dynamics have changed roughly 90-days out from the caucuses, thanks to former Vice President Joseph R. Biden’s shaky bid and Ms. Warren’s emergence as the liberal lion in the race.

For Mr. Buttigieg, Ms. Warren has served as a perfect foil by running on a populist liberal message that has thrilled activists while pushing middle-of-the-road voters in his direction.

“He is smart. He is intelligent, and his proposals are not as hard to the left as Elizabeth and Bernie [Sanders],” said Bruce Kaasa, 76, who is shopping for a candidate.

Mr. Kaasa cited Ms. Warren’s all-out push for “Medicare for All” — which would basically abolish private insurance — as a turnoff.

“I just don’t know if we are ready for Medicare for All because there are a lot of people that are content with the insurance they got,” the 76-year-old said.

Seeking to capitalize on that sentiment, Mr. Buttieig is running on a “Medicare For All Who Want It” proposal that offers consumers a government-backed option.

And he’s framing the debate as a battle over the freedom of choice.

“Some folks prefer a different plan and I am thinking about a lot of union members I’ve talked to who have negotiated really good health care plans and often … given concessions on wages in order to get that great health care plan,” he said at a town hall meeting here. “I am not going to command them to have to leave that to come onto ours. They will decide for themselves if it is a better plan.”

“So don’t listen to anybody who says you know it is either my way or the highway — Medicare for All, whether you want it or not,” Mr. Buttigieg said, jabbing Ms. Warren. “There is a better way. That is what I am proposing Medicare for All Who Want it. I think most voters want that and I think most Democrats want that.”

A New York Times/Siena College poll released last week showed that 42% of likely Democratic caucus-goers favor a Democrat who promises to replace the current health care system with Medicare for All and 56% favor a candidate who promises to improve the existing health care system.

The poll showed 51% are looking to support a Democrat with a more moderate brand, compared to 41% seeking a liberal warrior.

That includes voters like Laurie Davis, who said she is 90% certain she will caucus for Mr. Buttigieg, who served in Afghanistan in 2014 as a Navy Reserve officer during his first term as mayor.

“I like Mayor Pete because he is calm,” the 66-year-old said after catching him as a local Elks Lodge in Charles City. “He is so intelligent. He served our country. He is not going to give away everything. He is definitely gaining ground in Iowa.”

Scott Punteney, chairman of Pottawatomie County Democrats, said Mr. Buttigieg and Sen. Amy Klobuchar of Minnesota are grabbing the attention of voters who favor improving Obamacare, also known as the Affordable Care Act, rather than scraping it altogether.

“I think at one point we had so many of those candidates who were kind of like moderate, they kind of had the same ideas, that it was hard for people to latch onto a candidate, and maybe after the last series of debates those two have gained traction and have kind of finally risen up through that group of people,” Mr. Punteney said.

The increasing momentum and strong fundraising has allowed Mr. Buttigieg build out his ground game in Iowa. He now has over 100 staffers and over 20 offices across the state after kicking of the campaign with 4 staffers.

Doug Langfald said he was impressed by Mr. Buttigieg’s debate performances.

“I think he is young has some great ideas, has some new blood,” Mr. Langfald said. “In the debates, it was quite clear a few of them were not viable — they were not articulate for whatever reason.”

“I think it is going to come down to Buttigieg and Warren because Biden is a little too old school and Bernie is a little too radical,” the 66-year-old said. “So I think it is is going to Buttigieg and Warren.”

Doubt, though, lingers.

Joanna Johnson said she’s all-in for Mr. Buttigieg, but fears his sexuality — he is a married gay man — will hurt his chances of winning the presidency.

“I would like to think he could, but there are too many people that are prejudice against the fact that he has a husband,” she said, expressing concerns of how that will sell in South Carolina, where he is not well-known and struggling in polls. “Then you think of the people in South Carolina, how prejudiced and racist they are, I don’t know.”

Bob Cole, who is considering backing Mr. Buttigieg, lamented that his center-left views could “be part of his downfall.”

“He is in the moderate arena and the extremists are the ones who tend to pick the candidates,” Mr. Cole said. “They will rally behind their far-left candidates, and they are the ones that are passionate.”

Others, meanwhile, said they aren’t yet sold.

Wendy Johnson, 44, said she was left wanting after catching Mr. Buttigieg during a stop at local Elks hall in Charles City, describing his delivery as a bit “generic.”

“I was hoping today to learn more about him as a person,” she said. “In the town halls and the things I have seen with Elizabeth Warren, for example, she talks about who she is as a person, and it creates sincerity and integrity about her. I didn’t get that today from Mayor Pete. I feel like he is a very knowledgeable and everything, but I didn’t get that connection.”

“But I am still going to give him a chance,” the 44-year-old farmer said. “I am not counting him out.”

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