Tyler Raygor knocked on the door of a gray one-story house in a north Ames, Iowa, neighborhood and waited for a man in a hoodie and jeans to appear before entering his field.

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

Mr. Raygor, the state director of Americans for Prosperity Action, a super PAC that supports Ms. Haley, pointed out a recent poll in which Ms. Haley holds a wide lead over President Biden in an election contest, and highlighted her time as U.S. ambassador to the United Nations. He then presented Mr. Morton with a Haley campaign flyer. The pitch had an effect: Mr. Morton, 54, said he “will definitely take a closer look at Haley.”

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

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

And while her campaign’s efforts have produced better election results in other early voting states, including New Hampshire and South Carolina, she now sees an opportunity to secure a better-than-expected outcome in Iowa.

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

Ms. Haley got an eleventh-hour boost last month with support from Americans for Prosperity Action, a deep-pocketed organization founded by billionaire industrialist brothers Charles and David Koch. That support enabled access to donors and provided her bare-bones campaign with money for television spots and mail ads. (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 most of the racing ground to her better-financed rivals, the AFP Action apparatus has been resurrected, deploying its network of volunteers and staffers like Mr. Raygor across the state to knock on doors. and change your mind.

The super PAC has hired about 150 volunteers and part-time staff to survey the state, and the goal is to knock on 100,000 doors before the caucuses, said Drew Klein, a senior adviser at AFP Action. Since her endorsement, the organization has spent more than $5.7 million on pro-Haley advertising and canvassing efforts, and as of July had more than $74 million available, according to its 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 shrink as Mr. Trump maintains his dominant lead. A Des Moines Register/NBC News/Mediacom poll this month found Trump was the top choice 51 percent of Republicans likely a caucus, up from 43 percent in October.

Mr. DeSantis’s support in the state rose slightly to 19 percent, while Ms. Haley’s was unchanged and remained at 16 percent. Another Emerson College State Poll Last week found that Mr. Trump had support from half of Republican 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 backing him have spent significantly more time and money.

Florida’s governor has visited all 99 counties in Iowa, 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 is said that more than 801,000 doors have already been knocked on.

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

“Nikki Haley’s 11th-hour hire-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 success can be bought at the grassroots.”

Jimmy Centers, a Republican strategist in Iowa who is not aligned with the race, said AFP Action’s support and boots-on-the-ground operation could be the “missing link” for Ms. Haley. But he added that the group was running into a ticking clock.

“The open question here in Iowa is: Did Ambassador Haley peak about 30 days early, when she is already packing arrows and AFP doesn’t have time to catch up?” said Mr. Centers.

The super PAC claims its push is timely, as many people are just beginning to pay attention to the race for the Republican nomination. Mr. Raygor remembered that criticism from the Trump campaign who wondered whether AFP Action would come to the door at Christmas, given the late start.

‘Maybe not at Christmas, but we’ll knock on the 23rd. We will knock on the 26th,” said Mr. Raygor. “My team has experienced negative 30 degree wind chills before. Winter doesn’t scare us.”

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

“You’ll never get rid of Trump,” Barbara Novak said, rebuffing Mr. Raygor’s efforts when her bulldog barked at him from the window. “He did everything he said he was going to do.”

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

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

A recent trek through a Cedar Rapids neighborhood was even less fruitful. Cheryl Jontz, 60, and Kyla Higgins, 18, two part-time AFP Action staffers, split up to convert Ms Haley. Few people seemed interested in opening the door in the frigid morning temperatures, and those who did mostly said they would support Mr. Trump.

Ms. Higgins did reach a somewhat open-minded voter: Lisa Andersen, 52, who said 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 came up . to him.

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

A campaign spokeswoman for Haley said AFP Action’s support did not change the campaign’s strategy or ground game in Iowa, where her team has tried to reach every corner of the state.

The campaign has been going on for the past few days has made up for his final push before the caucuses. Ms. Haley completed a five-day tour of the state last week and has brought in more staffers, including Pat Garrett, a former adviser to the Iowa governor who will lead her Iowa press team.

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

“They are running a deft campaign,” Mr. Oman said, pointing to a small group of core staff and a group of volunteers who work long hours. “They’re making it a fight, that’s for sure.”