Tyler Raygor rapped on the door of a gray, one-story house in a neighborhood in northern Ames, Iowa, and waited until a man in a hoodie and jeans appeared before launching into his pitch.

The man, Mike Morton, said he was leaning toward voting for Gov. Ron DeSantis of Florida or former President Donald J. Trump in next month’s caucuses. But had Mr. Morton considered Nikki Haley, the former governor of South Carolina? No, Mr. Morton admitted, he hadn’t given her much thought.

Mr. Raygor, the state director for Americans for Prosperity Action, a super PAC supporting Ms. Haley, pointed to a recent poll showing Ms. Haley with a large lead over President Biden in a general election matchup, and highlighted her time serving as the U.S. ambassador to the United Nations. He then handed Mr. Morton a Haley campaign flier. The pitch had an effect: Mr. Morton, 54, said he “definitely will look closer at Haley.”

“If you didn’t come to my house,” he added, “I probably would overlook her a little bit more.”

With just under a month to go before January’s caucuses, Ms. Haley’s campaign — along with Americans for Prosperity Action — aims to capitalize on the momentum that her presidential bid has gained in recent months by reaching persuadable voters and firmly establishing her as the chief alternative to Mr. Trump for the Republican nomination.

And while her campaign’s efforts have yielded better polling results in other early voting states, including New Hampshire and South Carolina, she now sees a chance to secure a better-than-expected finish in Iowa.

“It’s ground game,” she told The Des Moines Register last week. “We’re making sure that every area is covered.”

Ms. Haley received an 11th-hour boost last month with the endorsement of Americans for Prosperity Action, a deep-pocketed organization founded by the billionaire industrialist brothers Charles and David Koch. That backing unlocked access to donors and infused her bare-bones campaign with funds for television spots and mail advertisements. (Under federal law, Ms. Haley’s campaign and the organization cannot coordinate, but the super PAC can support her with advertising, messaging and voter engagement.)

In Iowa, where Ms. Haley had ceded ground to her better-funded rivals for most of the race, the A.F.P. Action apparatus has whirred to life, deploying its network of volunteers and staff members like Mr. Raygor across the state to knock on doors and change minds.

The super PAC has enlisted about 150 volunteer and part-time staff members to canvass the state, and it aims to knock on 100,000 doors before the caucuses, said Drew Klein, a senior adviser with A.F.P. Action. It has spent more than $5.7 million on pro-Haley advertisements and canvassing efforts nationwide since endorsing her, and it had more than $74 million on hand as of July, according to the most recent financial filings with the Federal Election Commission.

Both Ms. Haley and Mr. DeSantis are fighting for a pool of undecided voters that could be dwindling as Mr. Trump maintains his dominant lead. A Des Moines Register/NBC News/Mediacom poll this month found that Mr. Trump was the top choice for 51 percent of Republicans likely to caucus, up from 43 percent in October.

Mr. DeSantis’s support in the state increased slightly, to 19 percent, while Ms. Haley’s did not change, remaining at 16 percent. Another Emerson College poll in the state last week found Mr. Trump had support from half of Republican caucus voters, while Ms. Haley had 17 percent and Mr. DeSantis had 15 percent.

But the reinforcements may be too late to overtake Mr. DeSantis in the state, where he and the groups supporting him have spent considerably more time and money.

The Florida governor has visited all Iowa’s 99 counties, and his well-funded ground operation, run almost entirely by Never Back Down, an affiliated super PAC, has been active in the state for months. It says it has already knocked on more than 801,000 doors.

Despite recent turmoil at that group — including the departure of its top strategist, Jeff Roe, just over a week ago — Never Back Down has established a foothold in Iowa, with a new emphasis on its turnout operation. Mr. DeSantis also has been endorsed by key figures there, including Kim Reynolds, the popular Republican governor, and Bob Vander Plaats, the influential evangelical leader.

“Nikki Haley’s 11th-hour rent-a-campaign gambit won’t work,” Andrew Romeo, a spokesman for Mr. DeSantis, said in a statement. “Only the Washington establishment,” he added, “would try to pitch that grass-roots success can be bought.”

Jimmy Centers, a Republican strategist in Iowa who is unaligned in the race, said A.F.P. Action’s endorsement, and its boots-on-the-ground operation, could be the “missing link” for Ms. Haley. But he added that the group was up against a ticking clock.

“The open question here in Iowa is: Did Ambassador Haley peak about 30 days too soon, where she is already taking arrows and A.F.P. doesn’t have time to catch up?” Mr. Centers said.

The super PAC argues its push is arriving at the right time because many people are just beginning to pay attention to the race for the Republican nomination. Mr. Raygor recalled criticism from the Trump campaign that wondered if A.F.P. Action would knock on doors on Christmas, given its late start.

“Maybe not on Christmas, but we’ll be knocking on the 23rd. We’ll be knocking on the 26th,” Mr. Raygor said. “My team’s knocked in negative-30-degree wind chills before. Winter does not scare us.”

But his recent swing through Ames illustrated the difficulty of a last-minute push. Of the six Republican voters who spoke with Mr. Raygor, one was already a Haley supporter and two said they were persuadable. The other three were firmly caucusing for either Mr. Trump or Vivek Ramaswamy and could not be swayed.

“You’re not going to get me off of Trump, ever,” said Barbara Novak, dismissing Mr. Raygor’s best efforts as her bulldog barked at him from the window. “He did everything he said he was going to.”

The reaction from Wanda Bauer, 72, suggested that the attacks lobbed at Ms. Haley by her rivals had shaped perceptions among at least some voters. Ms. Bauer said Ms. Haley was “big government” and “pro-giving money to Ukraine.”

“Just read the things she supports,” she said, “and you won’t be walking around passing out her brochures afterward, I guarantee you.”

A recent trek through a neighborhood in Cedar Rapids was even less fruitful. Cheryl Jontz, 60, and Kyla Higgins, 18, two part-time A.F.P. Action staff members, split up to proselytize Ms. Haley. But few people seemed interested in answering their doors in the freezing morning temperatures, and those who did mostly said they would be backing Mr. Trump.

Ms. Higgins did reach one somewhat open-minded voter: Lisa Andersen, 52, who said that she was leaning toward Mr. DeSantis or Mr. Trump, but that she would be willing to consider Ms. Haley if the former president’s legal troubles caught up to him.

“If Trump is in an orange jumpsuit, you have to make a different decision,” Ms. Andersen said.

A Haley campaign spokeswoman said that the support of A.F.P. Action had not changed the campaign’s calculus for strategy and a ground game in Iowa, where her team has been trying to reach all corners of the state.

In recent days, the campaign has been gearing up for its final push before the caucuses. Ms. Haley finished a five-day swing through the state last week and is bringing on more staff members, including Pat Garrett, a former adviser to the Iowa governor who will lead her Iowa press team.

David Oman, a Republican strategist and Haley supporter, said Ms. Haley was spending time where it most mattered: the six to eight metro areas where a majority of Iowa’s voters live.

“They are running a nimble campaign,” Mr. Oman said, pointing to a small group of core staff members and an assembly of volunteers working long hours. “They are making a fight out of it — that’s for sure.”