With temperatures threatening to dip below zero in Iowa on Monday, some of the voters preparing to caucus for Nikki Haley have already overcome a different hurdle: a long history of voting for Democrats.

At recent campaign events across Iowa, a number of Democrats and left-leaning independents said they saw Ms. Haley, the former governor of South Carolina, as a reasonable Republican who could move the country away from bitter partisanship and restore civility in national discourse. Many were drawn to her pledges to unite the country, and to work across the aisle on thorny issues such as abortion. Others are simply motivated by a fear of former President Donald J. Trump’s candidacy and the possibility that he will beat President Biden and regain the White House.

Joseph E. Brown Sr., who served two terms as an Iowa state senator in the 1970s and ’80s, said he was a registered Democrat for 50 years until he switched parties last month so that he could caucus for Ms. Haley.

“Now that I have my Republican card, I have to go visit my father’s gravesite here in town and apologize,” said Mr. Brown, who lives in Clinton, Iowa. He added that his father, a staunch Democrat and World War II veteran, always voted a straight party ticket.