The Florida governor’s field operation, one of the most expensive in modern political history, has met challenges from the outset, interviews with a range of voters and political officials revealed.Ron DeSantis’s battle plan against Donald J. Trump was always ambitious.This spring, the main super PAC backing Mr. DeSantis laid out a costly organizing operation, including an enormous voter-outreach push with an army of trained, paid door-knockers, that would try to reach every potential DeSantis voter multiple times in early-nominating states.Seven months later, after tens of millions of dollars spent and hundreds of thousands of doors knocked, one of the most expensive ground games in modern political history shows little sign of creating the momentum it had hoped to achieve.Mr. DeSantis’s poll numbers have barely budged. His super PAC, Never Back Down, is unraveling. And Mr. Trump’s hold on Republican primary voters seems as unshakable as ever. With time running out before the Iowa caucuses on Jan. 15, Mr. DeSantis, the governor of Florida, appears in danger of losing the extraordinary bet he made in outsourcing his field operation to a super PAC — a gamble that is testing both the limits of campaign finance law and the power of money to move voter sentiment.Never Back Down has spent at least $30 million on its push to reach voters in person through door-knocking and canvassing in early-primary states, according to a person with knowledge of its efforts — a figure that does not include additional tens of millions in television advertising. The organization has more than 100 full-time, paid canvassers in Iowa, South Carolina and New Hampshire, along with 37,000 volunteers.That ground game has increasingly centered on a do-or-die push in Iowa, where a long-shot victory could redeem the effort. Never Back Down has knocked on doors more than 801,000 times — including repeated visits — in Iowa, according to another person familiar with its work, a staggering number in a state of just 3.2 million people. The group has knocked on the doors of some potential DeSantis voters four times, with a fifth attempt planned before the caucuses, the person said.“I know they are doing the right things,” said Will Rogers, a Republican political organizer in Iowa who said Never Back Down had been to his door several times. But, he added, “it just doesn’t seem to be moving the needle at all.”Interviews with more than three dozen voters, local officials and political strategists across Iowa and beyond revealed that — even setting aside the internal disruptions at Never Back Down — the immense, coordinated effort to identify and mobilize voters for Mr. DeSantis has struggled from the outset.Mr. DeSantis’s decision to outsource his field operation to a super PAC was unusual, and tested the limits of campaign finance law.Christopher Smith for The New York TimesSome voters have been swayed by contact from the super PAC, but many remain unconvinced. Some said the door knockers were indifferent or rude, while others said the full-court press from Never Back Down felt inauthentic. And, in a particularly brutal twist, some of the door knockers openly told Iowans that they themselves were in fact Trump supporters.“From my point of view, it hasn’t been working,” said Cris Christenson, a businessman who lives in Johnston, a Des Moines suburb. Never Back Down has been all over his neighborhood, he said, and has knocked on his door three times.Mr. Christenson said he was “not anti-DeSantis,” describing him as “very bright.” But he is a firm supporter of Mr. Trump.“It really comes down to this — Trump is so wildly popular in the state that DeSantis doesn’t stand a chance,” he said.Spreading the wordJess Szymanski, a spokeswoman for Never Back Down, said the group had built “the largest, most advanced grass-roots and political operation in the history of presidential politics.”“With every voter we interact with on the ground, we constantly find strong support and new voters committing to caucus for Governor DeSantis,” she added. Door knocking is considered a particularly useful way not just to persuade and identify supporters, but above all to mobilize them to get to the caucuses or polls.The field operation is highly organized: Never Back Down has trained hundreds of people at an in-house boot camp in Des Moines that operatives call “Fort Benning.” There, recruits learn about the biography of Mr. DeSantis and his family, study his policies and record as Florida governor, and practice door-knocking techniques.Then, in groups — toting iPads with special software that contains details about likely voters — they spread out across Iowa and other early-nominating states.In Iowa, these paid door knockers have been joined by volunteer “precinct captains” — Never Back Down aims to have at least one captain in each of Iowa’s more than 1,600 caucus precincts by Jan. 15.Attendees at an Iowa Republican Party event in May were given information on Mr. DeSantis.Haiyun Jiang/The New York TimesNever Back Down is trying to reach Republicans in rural, heavily conservative areas like northwest Iowa, hoping that evangelical voters will embrace an alternative to the profane Mr. Trump.Quality control problemsSome of the challenges on the ground appear to stem from the operation’s size. The fact that it has been run by a super PAC rather than a campaign, and has relied largely on hired hands rather than volunteers, can make the outreach feel inauthentic, interviews with some caucusgoers showed.They described being put off or bemused by DeSantis campaigners who hailed from as far away as California. Douglas Jensen, a 38-year-old potential caucusgoer in rural northwestern Iowa who hasn’t decided which candidate to support, recalled being surprised to have a “very enthusiastic” man from Georgia pitch him on Mr. DeSantis at his house.Loren and Tina DeVries said they’d had door knockers from different campaigns stop by their house in Bettendorf. Some were locals — Ms. DeVries, 54, even knew the young woman who came to her door to stump for Vivek Ramaswamy personally.But the couple didn’t recognize the DeSantis door knockers, and recalled that they had been less than enthusiastic in their pitch.“The people that have come, I’m not sure if they’re there just to check a box or actually have a persuasive conversation,” Mr. DeVries, 53, said. “They’re not really doing a sell.”He still liked Mr. DeSantis, but Ms. DeVries remained undecided.Never Back Down, the super PAC supporting Mr. DeSantis, put out sign-up sheets to endorse him at an Iowa Republican Party event in Cedar Rapids.Haiyun Jiang/The New York TimesDeSantis campaign materials at a restaurant in Tipton, Iowa.Jordan Gale for The New York TimesNumerous other voters have also reported lackadaisical efforts, fruitless repeat knocking and bad attitudes from door knockers. Over the summer, a paid Never Back Down canvasser in South Carolina was dismissed after he was caught making lewd remarks about a homeowner, The Washington Post reported.The super PAC has dismissed employees and volunteers who failed to meet targets for door knocking and other measures of engagement, according to people who worked with the group.Fierce competition, and a looming favoriteOther campaigns are trying to capitalize. The political network founded by the Koch brothers, Americans for Prosperity Action, which endorsed Nikki Haley last month, is aiming to knock on 100,000 doors in Iowa before the caucuses. The group is hoping that a more finely honed message, spread by the small group of well-trained volunteers and paid staff, will be enough to overcome the flood of outreach from Never Back Down.Tyler Raygor, A.F.P.’s state director, said the fact that Mr. DeSantis had been stagnant in state polls despite the huge canvassing effort cast doubt on how effective his messengers were.“It just begs the question of: ‘Who are you having out on the doors? How well are you training them?’” Mr. Raygor said.The Trump campaign has also put down roots in Iowa, though its efforts have focused more on training its 1,800 caucus captains and pushing them to persuade their friends and neighbors to caucus for Mr. Trump. Still, the campaign has reached several hundred thousand voters in Iowa through mail advertisements and door knocking, according to a person familiar with the efforts.Indeed, it seems possible that no amount of door knocking could surmount Mr. DeSantis’s biggest challenge: He is not Donald Trump.Former President Donald J. Trump still leads in polls of Iowa caucusgoers by double digits. Jordan Gale for The New York TimesJeanette Hudson, 82, of Pella, Iowa, said she and her husband, both loyal Trump supporters, had been visited at home by a “pleasant young woman” who asked if they were going to caucus for Mr. DeSantis. Ms. Hudson said they were not.The woman smiled, thanked them and left.Persuading the unconvincedDavid Polyansky, the DeSantis deputy campaign manager, said door knocking was meant to drive turnout on caucus night, not to juice poll numbers.“It gives you the chance to not only identify who might be a DeSantis supporter, but also to bring them into the fold and make sure they are going to turn out on the 15th,” he said, arguing that it was too soon to judge the effectiveness of Never Back Down’s door-knocking operation.Mr. DeSantis’s allies say that many Iowans remain undecided, and that a major part of the ground game, in the weeks ahead, is to tip them to their side.Rachel Mummey for The New York TimesIn New Hampshire, the way that Mr. DeSantis won the support of Hilary Kilcullen, 76, a physician assistant in Concord, is a model that Never Back Down hopes to emulate.Ms. Kilcullen, a Republican, said a young man had knocked on her door to tell her about Mr. DeSantis. The canvasser, who had flown up from Miami, told Ms. Kilcullen that she could rely on Mr. DeSantis in the event of a terrorist attack or other disaster.The conversation didn’t flip Ms. Kilcullen, who had grown tired of Mr. Trump, into a DeSantis supporter. But she valued the personal touch.“In this day and age, when everything has gone digital and virtual, I was impressed,” Ms. Kilcullen said. “If DeSantis could capture this passionate, young person’s attention, that means something.”Then, after hearing Mr. DeSantis speak in person this month at a town-hall event — and being impressed by his command of policy — she decided he had earned her vote.But others have yet to be convinced.One undecided caucusgoer in Iowa, Edith Hull, a 73-year-old retired farmer from Ottumwa, said she had a positive experience with a DeSantis door knocker recently.“He was a real nice young man,” she said. “And he didn’t pressure me or anything.” When he left, he gave her a large placard to hang on her doorknob, and reminded her to caucus.Asked if she felt any differently about Mr. DeSantis afterward, she said, “About the same.”Reporting was contributed by More