Through the early days of the election cycle, Republican voters and elected officials in Iowa said they saw little of Ms. Haley. She was polling in the single digits and lagging behind her rivals on fund-raising, making it difficult to campaign in a rural state that requires more time and money to cover ground. But her campaign has been gradually adding staff and building out her Iowa footprint since the summer. Last month, her Iowa team added two new members: Hooff Cooksey, Governor Reynolds’s campaign manager during her 2018 run, and Troy Bishop, the 2022 field director for Senator Chuck Grassley.

Before the most recent Republican debate in Miami, a group of Iowa farmers and agricultural leaders announced their support for Ms. Haley’s bid, citing her tough talk on China, stances on renewable energy and pledges to repeal government regulations. On Tuesday, she released a slate of more than 70 endorsements from elected officials and community and business leaders.

In interviews, Ms. Cournoyer and some Haley endorsers argued that though much of Mr. Trump’s support in Iowa is unmovable, Ms. Haley had the chance to make up ground with independents and moderates. Bob Brunkhorst, a former state senator and former mayor of Waverly on that list, said her team had been astute about not spending too much early in the cycle and waiting to expand in the state.

“They know how the game is run,” he said, “and when to peak.”

On Monday, Ms. Haley’s campaign announced it would be spending $10 million in television, radio and digital advertising in Iowa and New Hampshire starting in the first week of December — its first investment in advertising of the cycle and an amount so far outpacing the DeSantis campaign in the coming months.

In a press call the next day, Mark Harris, the lead strategist for Stand for America, the super PAC backing Ms. Haley, said the PAC had been helping level the playing field for her in Iowa. (Mr. DeSantis’s allied super PAC, Never Back Down, has invested roughly $17.7 million in the state covering this year and into January, and Stand for America has committed $13.6 million, according to AdImpact, a media-tracking firm.) He projected further growth and contended the DeSantis campaign had backed himself into a corner.

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