Despite spending far more time campaigning across the must-win state, Ron DeSantis still trails Donald Trump by double digits. And now Mr. Trump is stepping up his visits.On paper, Gov. Ron DeSantis of Florida is doing everything that a Republican presidential candidate should do to win Iowa.He is doggedly crisscrossing the state, visiting 58 of its 99 counties so far and vowing to make it to the rest. He is meeting voters at small-town churches, meeting halls, county fairgrounds and ice-cream parlors, heavily courting evangelicals and racking up endorsements from influential faith leaders and local politicians. His super PAC is building a formidable get-out-the-vote operation and says it has reserved $13 million in television ads in Iowa through Thanksgiving.For Mr. DeSantis, who is trailing former President Donald J. Trump in Iowa by double digits, the state has become a must-win. Mr. Trump, who has campaigned sparingly here, appears to know it. The Trump campaign recently announced that he would visit Iowa five times in the next six weeks, including stops on Wednesday, in a clear attempt to scupper Mr. DeSantis’s bid for the presidency with a resounding victory in the Jan. 15 caucuses, the first votes of the race for the nomination.Mr. Trump’s enduring popularity with the Republican base — so strong that the former president has recently felt comfortable veering away from the party’s orthodoxy on abortion — is only one of Mr. DeSantis’s major hurdles in Iowa. The other is his lack of light-up-the-room charisma and folksy authenticity, qualities that seem required, at a minimum, to beat an established star like Mr. Trump.“He’s very cerebral, very smart,” said John Butler, 75, an accountant from Pella, Iowa, who heard Mr. DeSantis speak on Saturday at a gathering of Christian conservatives in Des Moines. “But it feels like it can be hard to get to know him.”For now, Mr. DeSantis’s top advisers say they are planning a steady diet of the grind-it-out approach that worked for the Republican victors in the 2008, 2012 and 2016 Iowa caucuses — none of whom, notably, went on to capture the party’s nomination.“Winning an Iowa caucus is very difficult,” David Polyansky, Mr. DeSantis’s deputy campaign manager, said in an interview this month. “It takes a tremendous amount of discipline. It takes an incredible amount of hard work and organization, traditionally. So much so that even in his heyday, Donald Trump couldn’t win it in 2016.”A campaign stand for former President Donald J. Trump was set up at a tailgate event this month in Nevada, Iowa.Jordan Gale for The New York TimesMuch of the DeSantis strategy mirrors the approach taken by the last three Republicans to win contested caucuses in Iowa: former Gov. Mike Huckabee of Arkansas, former Senator Rick Santorum of Pennsylvania and Senator Ted Cruz of Texas, all social conservatives who trekked to practically every corner of the state. Mr. Cruz — not exactly a ball of white-hot magnetism himself — beat Mr. Trump here in 2016, an effort in which Mr. Polyansky played a key role.“Governor DeSantis is doing the 99-county tour,” said Senator Joni Ernst of Iowa, who appeared with Mr. DeSantis on Saturday at a meet-and-greet at a county historical society in her hometown, Red Oak. “He’s meeting with those Iowa voters. That makes a difference.”And Mr. Trump may be giving Mr. DeSantis openings to press his case in the state.In an interview broadcast on Sunday, Mr. Trump called a six-week abortion ban that Mr. DeSantis signed in Florida a “terrible thing.” Iowa passed a similar law that is widely popular with social conservatives. Mr. DeSantis struck back on Monday in an interview with Radio Iowa, saying, “I don’t know how you can even make the claim that you’re somehow pro-life if you’re criticizing states for enacting protections for babies that have heartbeats.”The former president has also spent few days campaigning in Iowa so far, and he was booed when he appeared this month at the Iowa-Iowa State football game.“They’re jittery, they’re nervous, and they absolutely should be,” Mr. Polyansky said of the Trump campaign. “At the end of the day, it’s going to be a very tight race in Iowa. And the former president losing there seriously damages the sheen of invincibility that they are trying to project.”Steven Cheung, a spokesman for the Trump campaign, said Mr. Trump would “put the pedal to the metal” in Iowa, even though he has a commanding lead.“We don’t play prevent defense,” Mr. Cheung said in a statement. “President Trump’s aggressive upcoming schedule in Iowa reflects his continued commitment to earning support in the state one voter at a time.”One of Mr. DeSantis’s biggest challenges may be showing voters that he is not as painfully awkward as his critics suggest.Rachel Paine Caufield, a professor of political science at Drake University in Des Moines, has seen Mr. DeSantis appear at roughly 10 events so far this cycle. She said that his small-town approach made sense in Iowa but that he himself might not be the right candidate to execute it. She has been particularly struck, she said, by how he interacts with voters.“He always looks miserable until he’s directly in front of a camera about to take a selfie,” said Dr. Paine Caufield, who has written a book about the Iowa caucuses.On Twitter, a cottage industry has sprung up turning Mr. DeSantis’s most awkward moments into viral memes. There was the time he told a young girl at a county fair in Iowa that her Icee probably had a lot of sugar. The painful way his face contorted when he was reminded that Mr. Trump led him in the polls. And, of course, the bizarre, almost body-racking laughs — his head thrown violently back, eyes screwed shut, mouth agape — he uses to herald jokes from voters.New York magazine and Vanity Fair have packaged those interactions into clickbait listicles. They have become fodder for late-night comedians. The Onion, a satirical news site, has turned Mr. DeSantis into a regular punching bag (“DeSantis Has Surprisingly Smooth Verbal Exchange With Iowa State Fair Corn Dog,” one headline read).Even his super PAC, Never Back Down, reminded Mr. DeSantis that he should be “showing emotion” when discussing his wife and children, in an unexpectedly public memo about last month’s debate.Mr. DeSantis’s super PAC, Never Back Down, has been integral to his campaign in Iowa, and it has reserved $13 million in television ads there through Thanksgiving.Jordan Gale for The New York TimesBut on the campaign trail, where he is often accompanied by his wife, Casey, a former local television anchor, and their three small children, Mr. DeSantis has seemed plenty likable, voters say. Even some Trump supporters don’t find him to be a stiff. They just like Mr. Trump better and wish the Florida governor had waited to run until 2028.“I saw a very confident spokesman for what he believes in,” said Madeline Meyer, 85, a retiree who heard Mr. DeSantis speak at a fund-raiser in Iowa last month but said she planned to stick with the former president. “He’s got a good voice and a nice, young family.”In a Fox News interview last weekend, Mr. DeSantis called criticisms of his demeanor a “bogus narrative.”Kristin Davison, Never Back Down’s chief operating officer, said the group’s messaging in Iowa would zero in on Mr. DeSantis’s plans for immigration and the economy, which polling shows are top issues for Republicans.“We’re focusing on amplifying what the governor has said he will do for voters,” Ms. Davison said in an interview.Mr. DeSantis has also tried to tailor his appeal more specifically to Iowa voters in recent trips, after heavily focusing his initial pitch on his record in Florida. He has noticeably adjusted his stump speech to talk less about Florida and more about what his priorities would be as president.But the governor clearly finds it hard to leave his home state behind.As he walked through an Iowa cattle ranch over the weekend, a gust of wind blew his blazer open, revealing that its lining had been stitched with images of Florida’s state flag.Maggie Haberman More