Campaigning in New Hampshire on Wednesday, former Gov. Nikki Haley of South Carolina said that voters there would “correct” the result of the Iowa caucuses — the night before she was scheduled to appear for events in Iowa.

“You know Iowa starts it. You know that you correct it,” Ms. Haley said, prompting laughter from the crowd of New Hampshire voters. “And then my sweet state of South Carolina brings it home.”

Local campaign surrogates for Gov. Ron DeSantis of Florida, who is vying with Ms. Haley for second place in Iowa polls for the Republican presidential nomination, seized upon the remark as dismissive of the state’s first-in-the-nation balloting, scheduled for Jan. 15.

Gov. Kim Reynolds, who has endorsed Mr. DeSantis, said, “I trust Iowans to make their own decisions. No ‘corrections’ needed.” Bob Vander Plaats, the Iowa evangelical leader who has also thrown his support behind Mr. DeSantis, called Ms. Haley’s quip an “admission of getting beat in the Hawkeye State.”

Mr. DeSantis and Ms. Haley are scheduled to participate in back-to-back town halls Thursday night in Iowa. The events, to be broadcast live on CNN, will be among the few remaining opportunities for the two candidates to draw away support from former President Donald J. Trump.

Ms. Haley’s teasing remark also reflects her dim chances of a victory in Iowa, where Mr. Trump is the overwhelming favorite; he is polling around or slightly below 50 percent support. Ms. Haley and Mr. DeSantis are polling below 20 percent in Iowa in a virtual tie for second place.

In contrast, Ms. Haley has decisively risen from the pack of Mr. Trump’s rivals in New Hampshire. Recent polls there have shown her in second place far above other candidates, except for Mr. Trump.

Ms. Haley’s quip also reflects the perils of campaigning across state lines in quick succession: Remarks playing to the local crowd in one state can become a liability in the next.

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