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.