VINTON, Iowa — Sen. Elizabeth Warren’s surging campaign is running into a dose of reality in this crucial nominating battleground where caucusgoers increasingly raise concerns that she is too radical for their liking and too liberal to topple President Trump in the general election.

The additional scrutiny comes with being widely viewed as the candidate to beat in Iowa, and it will test Ms. Warren’s mettle over the final three-month stretch of the campaign in the state. The race remains fluid, and many undecided voters are looking for a more “sensible” and “common-sense” alternative.

“I think Warren is too far out there,” said Joe Roman, a retired steelworker from Cedar Rapids. “You can’t promise everything and get away with it.”

The 64-year-old said Ms. Warren is promising “too much free stuff” and “has to be more realistic” about how she would pay for her vision.

Former Secretary of State Tom Vilsack, who served as governor from 1999 to 2007, said he hopes voters start pressing Ms. Warren on policy and spending plans.

“I think Sen. Warren, in particular, and Sen. [Bernard] Sanders have to explain to a lot of voters, practical voters, people out in the small towns, who want to know ‘How are you going to get this passed?’” Mr. Vilsack said.

“Where are the 60 votes in the Senate to actually do all these wonderful things?

“We are now entering a stage in a race where people are going to get real about all of this,” he said. “All the fun time is gone.”

‘We need big ideas’

Ms. Warren is countering the bubbling skepticism by more forcefully and unapologetically defending her crusade for “Medicare for All,” the Green New Deal and a new tax on the assets of the uber-wealthy.

“We need big ideas, and just as importantly we need to be willing to fight for those ideas,” Ms. Warren said at a town hall event in a high school cafeteria over the weekend.

“Look, I get it. It is easy to walk away from big ideas and make yourself sound so sophisticated and so smart when you do it. But when we give up on big ideas, we give up on the people whose lives would be touched by those ideas. And those people are already in a fight,” she said.

The comments were a swipe at her less-liberal rivals — perhaps no one more so than Mayor Pete Buttigieg of South Bend, Indiana, who has been on the rise in Iowa and who is betting that voters are more interested in returning “sanity” to Washington than in transformational change.

“The biggest difference is I think we can deliver major, meaningful, bold change to move this country forward in a way that galvanizes an American majority instead of polarizing our country further,” Mr. Buttigieg said Sunday on ABC’s “This Week.”

Mr. Buttigieg faces his own challenges: Can he convince voters that as the mayor of a relatively small Midwestern city that he has the experience to lead the nation? Can he win over black voters who have shied away from his bid? And are voters ready to elect gay man as president?

“The Trumpian Christian right will kill him — right, wrong or indifferent,” said Ellis Van, who nonetheless is considering supporting Mr. Buttigieg.

‘Fighting is [not] the point’

Ms. Warren and Mr. Buttigieg shined over the weekend, drawing the most raucous crowds to the Iowa Democratic Party’s biggest event of the year.

“We will fight when we must. But I will never allow us to get so wrapped up in the fight that we start to think fighting is the point,” Mr. Buttigieg said in his speech. “The point is what is on the other side of the fight, and what is on the other side of that fight is the hope of an American experience defined not by exclusion, but by belonging.”

Ms. Warren outlined a competing approach in her address.

“This is a time of crisis, and the media pundits, Washington insiders, even some people in our own party don’t want to admit it,” she said. “They think running some vague campaign that nibbles around the edges is somewhat safe.

“I’m not running some consultant-driven campaign with some vague ideas that are designed not to offend anyone,” she said.

‘She just grates on people’

The back-and-forth showed how the contours of the race have changed.

Ms. Warren has seized the far-left mantle from Sen. Bernard Sanders of Vermont, and Mr. Buttigieg, as least for the moment, has overtaken former Vice President Joseph R. Biden as the favorite of voters looking for a more “moderate” candidate.

“I am most impressed with Elizabeth Warren. I just think she is too smart to pass up,” said Lyn Hopkins, 67.

JoAnna Trierweiler, who made the trip from Michigan, which Mr. Trump carried in 2016, said she appreciates the role Ms. Warren has played in thrusting important issues to the forefront of the 2020 debate, but she added that Mr. Buttigieg has a much more palatable approach.

“Think about it this way: Warren is an activist,” Ms. Trierweiler said as she walked with Buttigieg supporters and a marching band through the streets of Des Moines. “She is passionate about making a dramatic change in a very short period of time.

“Pete is an advocate,” she said. “He knows that we need change. He knows that it takes a lot of people to make change, and he knows that we can’t do it by flipping a switch.”

Biden backers said a Warren nomination would doom the party’s chances in 2020.

“If she gets the nomination, we are going to get our butts kicked,” said Dave Schmidt, a retired superintendent from Ankeny, Iowa. “People don’t like her for whatever reason. She just grates on people. I don’t know what it is. I can’t put my finger on it.”

The presidential race has entered a new phase, and the TV ad wars are intensifying.

The top contenders have started to cast aside the niceties, hone their messages and sharpen their attacks just over 90 days out from the first-in-the-nation contest.

Former Rep. Beto O’Rourke’s decision to pull the plug on his campaign has shifted attention to how much longer other lower-tier candidates, including former Housing and Urban Development Secretary Julian Castro, can keep their flagging campaigns afloat. Party insiders say Sens. Kamala D. Harris of California, who has gone all-in on a strong showing in Iowa, and Cory A. Booker of New Jersey have about a month left to make their mark.

‘Upset the system too much’

The bull’s-eye on Ms. Warren’s back has expanded since she captured the polling lead in Iowa about a month ago, and the debate has intensified over her Medicare-for-All plan, which she says costs $20.5 trillion over 10 years and won’t increase taxes on the middle class.

At a town hall Saturday, Ms. Warren was pressed on how her plan would impact people suffering from chronic illnesses.

“This will be about strengthening America’s middle class. It will be about people who won’t have to keep a job they don’t like because it is the only way they have to keep their health insurance,” she said. “It will be about freeing people up to start the little business you want to start, and this will be about nobody has to wake up in the middle of the night wondering how they are going to pay their health care bills.”

Voters, including her supporters, say they oppose Ms. Warren’s push for a variety of reasons.

“I think it is too costly, and I think a lot of people have very good health insurance,” said Steve Arnold, a 67-year-old former teacher who thinks Ms. Warren should stay in the Senate. “I just think it would upset the system too much.”

Mr. Schmidt, the retired superintendent, said Democrats are better off fixing Obamacare than pushing for a single-payer, socialist-style health care system.

“If we nominate a candidate who is going to advocate for that, Democrats are going to lose the election,” he said. “It is not going to go nationally. Trump has done a good job of labeling it as socialism, and that is going to scare a lot of people who maybe aren’t quite as informed as they should be.”

Bob and Linda Sprengeler said Ms. Warren could be their preferred pick and said they “absolutely” support her health care push, though they expressed concern that it could be a bridge too far for much of the country.

“If I lived on the East Coast or maybe on the West Coast, I could see people being more accepting of universal health care for all and starting right away,” said Mr. Sprengeler, 82, adding that the idea is a tougher sell in the Midwest. “It takes time for that to happen.”

Mrs. Sprengeler said she started as a Warren backer but now is wondering whether she could be “too left-wing” for the general public. She said she is giving Sen. Amy Klobuchar of Minnesota a good look.

“So right now, believe it or not, it is kind of a toss-up between Klobuchar and Warren. Because Klobuchar is more middle of the road, she might appeal more to the general public, and I do not want Trump or the Republicans to win,” she said. “All civilizations die, and we are dying, and we need to change it.”

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