Negative mailers are overstuffing Iowa mailboxes. Attack ads are cluttering the airwaves. And door knockers are fanning out from Des Moines to Dubuque and everywhere in between.

The Iowa caucuses, the first contest in the Republican nominating calendar, are poised to play an especially consequential role in 2024. But with only 49 days to go, Donald J. Trump’s top rivals are running out of time to catch him as Ron DeSantis and Nikki Haley thrash each other in the final sprint to the starting line.

Far ahead in national polls, Mr. Trump is aiming for an emphatic victory on Jan. 15 in Iowa that could serve as an early knockout punch. He leads in public surveys in the state by a margin twice as large as the most competitive contest in the last 50 years.

Mr. DeSantis, the Florida governor, is betting on Iowa to pierce Mr. Trump’s growing aura of inevitability — and to reassert himself as the main rival to short-circuit Mr. Trump’s third run for president. Mr. DeSantis, who won the backing of the state’s popular Republican governor, has been barnstorming across all of Iowa’s 99 counties, bolstered by an army of door knockers paid for by his related super PAC.

On Saturday, Mr. DeSantis will visit his final county with an event in Newton held at the Thunderdome, a venue whose name appropriately captures the increasing acrimony and intensity of the race in the state. Mr. Trump will be in Cedar Rapids that same day.

For much of the year, the DeSantis team had insisted the 2024 primary was a two-man race. But Ms. Haley, the former United Nations ambassador, has ridden the momentum of her debate performances to transform it into a two-man-plus-one-woman contest.

“The more people see of Nikki Haley the more they like her,” said Betsy Ankney, Ms. Haley’s campaign manager. “The more they see Ron DeSantis, the less they like him.”

Now Ms. Haley, who wore a T-shirt emblazoned with the words “Underestimate me — that’ll be fun” to the Iowa State Fair, is seeking to snuff out Mr. DeSantis at the very start. If she can best Mr. DeSantis in Iowa, his strongest early state, her team believes Ms. Haley would be positioned to emerge as the singular Trump alternative when the calendar turns to two friendlier terrains — New Hampshire, where she has polled in second place, and her home state, South Carolina, where she served as governor.

Revealingly, Ms. Haley’s allied super PAC has spent $3.5 million on ads and other expenditures attacking Mr. DeSantis in the last two months in Iowa and New Hampshire, according to federal records, but not a dollar explicitly opposing Mr. Trump despite his dominant overall lead.

“Nikki Haley and her donors are greedily wasting millions of dollars targeting Ron DeSantis in Iowa,” said David Polyansky, deputy campaign manager for Mr. DeSantis, who called that spending a political gift to Mr. Trump because the likeliest second choice of DeSantis supporters is not Ms. Haley but the former president.

Mr. Trump’s team has gleefully greeted the battling. James Blair, national field director for Mr. Trump, said Ms. Haley and Mr. DeSantis were “trying to bludgeon themselves for the title of first loser.”

“The biggest win in Iowa ever is 12 points so anything above that is setting a record,” Mr. Blair added, arguing that even an upset in Iowa would only prove a blip given the former president’s superior organization across the rest of the states on the calendar.

Iowa always plays a critical in narrowing a presidential primary field but this year it could determine whether there is much of a contest at all. The Trump campaign has told supporters that it has booked its first significant television ads to begin in Iowa on Dec. 1, and Vivek Ramaswamy, the entrepreneur, has pledged to also spend millions in the final weeks even as his standing has slid since the summer.

“Almost everybody is pushing the chips into the middle of the table in Iowa,” said David Kochel, a Republican strategist with years of experience in the state. Only Chris Christie is bypassing Iowa, hoping a muddled result could allow him to break through in New Hampshire.

As the candidates vie for votes, their strategists and spinmeisters are seeking any possible advantage in the unseen but critical contest of expectations-setting. Those who surprise or surpass where they are expected to finish typically emerge with the most momentum — and money.

“If he doesn’t win Iowa, Ron DeSantis has no rationale to move on,” said Ms. Ankney, Ms. Haley’s campaign manager.

Mr. DeSantis’s support has mostly collapsed in New Hampshire, where one recent poll showed him in fifth place. The state’s voters are typically more moderate than Iowa’s and the lack of a serious Democratic primary means independents could flood the contest, which could help Ms. Haley or Mr. Christie.

The Haley campaign has announced plans to spend $10 million on television, radio and digital ads in Iowa and New Hampshire (about $4.25 million has actually been reserved on television so far). The DeSantis campaign has announced plans to spend $2 million on Iowa television ads.

On the trail, Mr. DeSantis has been saying in increasingly blunt terms that Mr. Trump would lose a rematch against President Biden. But the energy behind that argument has diminished both because Mr. Biden has slipped in the polls and because Ms. Haley has tended to fare even better than either Mr. Trump or Mr. DeSantis in such a hypothetical matchup. In some cases, Mr. DeSantis has fared worse than Mr. Trump, too.

The DeSantis super PAC has spent 10 times more money criticizing Ms. Haley in ads and other expenditures than against Mr. Trump, records show. But in private, Mr. DeSantis and his wife, Casey, have expressed disapproval of those ads, according to two people familiar with their remarks. Several DeSantis allies recently created a new entity to explore fresh avenues of attack on Ms. Haley but the decision has caused more turmoil on the team, with the chief executive abruptly resigning last week.

In Iowa and beyond, Mr. Trump’s team has almost exclusively focused on Mr. DeSantis, whom Mr. Trump has treated as his only serious challenger throughout 2023. Mr. Blair said it was notable how much the DeSantis operation was spending attacking Ms. Haley rather than “trying to grow Ron’s image or hurt the president — because they’ve given up on those things.”

“They’re just trying to stop Nikki Haley from coming in second,” Mr. Blair added.

There are two debates planned before the Iowa caucuses that could still jostle the dynamics. Only the first, on Dec. 6 in Alabama, has been announced; the second is planned for January in Iowa. Mr. Trump has said he won’t participate in any debates and his team has tried to pressure the Republican National Committee to cancel the rest.

The other wild card is the much-discussed door-knocking operation of Never Back Down, the pro-DeSantis super PAC that said it had 26 paid political staff members in the state and thousands of volunteers. The group says it has knocked on almost 677,000 doors to date — including three times on every targeted home.

Jeff Roe, the chief strategist for Never Back Down, has told people that he believes the group’s door-knocking push could be worth as much as 10 percentage points on caucus day, according to a person who has heard the pitch.

Caucuses, which occur at 7 p.m. on a typically frigid Monday evening, are far more involved than regular elections and tend to benefit the most organized candidates. But some are skeptical that organizing could give such a large lift.

“DeSantis seems to have the best groundwork going out here but it’s nothing compared to what people in the past have had,” said Andy Cable, a longtime Republican activist in Hardin County, which is north of Des Moines. “Trump doesn’t need the groundwork. His people will just show up. Nikki has come on late but I’m not sure she has the actual organization on the ground to actually do it.”

Trump campaign officials say their operation has already amassed 50,000 signed cards committing to caucus for him, and 1,800 “caucus captains” for the more than 1,600 precincts. The DeSantis campaign said it had more than 30,000 people who had committed to caucus for him. The Haley campaign declined to provide any such data points.

For Mr. DeSantis, the endorsement of Kim Reynolds, the state’s Republican governor, has given him a jolt of energy and she plans to campaign heavily for him through the caucuses, including next Saturday in Newton, Iowa.

A television ad featuring Ms. Reynolds is already running. “He gets things done,” she says in the spot.

Mr. DeSantis has also won the backing of Bob Vander Plaats, an influential evangelical leader in the state who has endorsed the last three Iowa caucus winners in contested races — Ted Cruz in 2016, Rick Santorum in 2012 and Mike Huckabee in 2008, all of whom lost the eventual nomination.

White evangelical voters are seen as crucial to any potential DeSantis breakthrough, and the Trump campaign has sought to organize support among church leaders, announcing that their total faith leader endorsements topped 150 on the same afternoon that Mr. Vander Plaats made his announcement.

Judging from campaign stops, Mr. DeSantis’s 99-county tour does appear to have created some momentum in Iowa. He regularly draws crowds of 50 to 100 people to small-town events at pizza shops, coffee houses and family farms, taking questions and posing for photos.

“I’ve been a Trump man all along, but I liked what DeSantis had to say,” said Ev Cherrington, 86, who heard Mr. DeSantis speak at a barbecue restaurant in Ames, Iowa, this month and said he was now considering backing him, largely because of the laundry list of policy ideas that Mr. DeSantis had recited.

But outside of the bubble of Mr. DeSantis’s bus tour, a different reality sets in. As Mr. DeSantis visited his 98th Iowa county a week ago after holding around 10 small public events over three days, Mr. Trump appeared at a rally in a high school gym in Fort Dodge, Iowa. He drew roughly 2,000 people, according to The Associated Press — more than all of Mr. DeSantis’s events combined.

Nicholas Nehamas and Maggie Haberman contributed reporting.