Representative Nancy Mace, Republican of South Carolina, on Tuesday defeated a well-funded primary challenger, putting her on track to win a third term. Her resounding victory also dealt a major blow to former Speaker Kevin McCarthy’s efforts to exact political retribution against those who voted to oust him.

Ms. Mace, 46, who once leaned center on social issues, won a Democratic seat in 2020 and claimed that all of former President Donald J. Trump’s accomplishments had been “wiped out” by his behavior on Jan. 6, 2021. But she has made a hard tack to the right over the past year as she has tried to game out her political future.

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