CONWAY, S.C. — Tom Rice, the South Carolina congressman who was one of 10 House Republicans to vote to impeach President Donald J. Trump after the Jan. 6 attacks, has a catchall term to describe the former president’s crusade against him: Trump’s Very Presidential Traveling Revenge Circus.

Mr. Trump has made unseating Mr. Rice, a five-term congressman, one of his top priorities in the state’s primary elections on Tuesday. He threw his support in the Republican primary for Mr. Rice’s seat behind State Representative Russell Fry, calling into a rally for Mr. Fry this week and describing Mr. Rice as a “back-stabbing RINO,” the acronym for Republican in name only, a conservative slur.

“He lifted up his hand and that was the end of his political career — or we hope it was,” Mr. Trump said of Mr. Rice’s vote to impeach him.

In a 35-minute interview on Friday alongside his wife, Wrenzie, after a barbecue luncheon campaign event, Mr. Rice sounded every bit like a man in the fight for his political life. His campaign is not counting on an outright win against Mr. Fry but is instead bracing for a tough runoff with him.

But while some, after crossing Mr. Trump, have tried to salvage their political careers by walking back their comments or retiring from Congress, Mr. Rice has doubled down.

“To me, his gross failure — his inexcusable failure — was when it started,” Mr. Rice said of the Jan. 6 riot. “He watched it happen. He reveled in it. And he took no action to stop it. I think he had a duty to try to stop it, and he failed in that duty.”

Mr. Rice, a pro-business conservative and self-proclaimed Chamber of Commerce Republican, helped craft Mr. Trump’s sweeping new tax code in 2017. Five years after those reforms and 17 months after the Jan. 6 attacks, he argued that the former president had overstayed his welcome in the G.O.P.

“He’s the past,” Mr. Rice said of Mr. Trump. “I hope he doesn’t run again. And I think if he does run again, he hurts the Republican Party. We desperately need somebody who’s going to bring people together. And he is not that guy.”

Mr. Rice said the Jan. 6 prime-time hearing on Thursday night, which featured footage of the Capitol riots and incriminating testimony from close Trump associates, “puts an exclamation point on what we did,” referring to the 10 House Republicans who backed impeachment.

In the days after the riot at the Capitol, Mr. Rice said, he considered voting to impeach Mr. Trump, and spent that Saturday and Sunday in his home congressional district reading the dozens of stories he had asked his staff to send him about the president’s whereabouts on Jan. 6. As he learned of the president’s refusal to stop the attack, he became incensed. When it came time for his vote, he said he had “zero question in my mind” about whether Mr. Trump should be held accountable.

“I did it then,” he said. “And I will do it tomorrow. And I’ll do it the next day or the day after that. I have a duty to uphold the Constitution. And that is what I did.”

Mr. Rice did not vote to certify the election, however, saying he had become concerned about ballot discrepancies in Pennsylvania that were outlined in a letter to House Republican leadership.

During a House Republican meeting one month after the Capitol riots, he defended Liz Cheney for her vote to impeach and criticized Kevin McCarthy, the minority leader, for his continued embrace of the former president, according to audio from the exchange.

“Kevin went to Mar-a-Lago this weekend, shook his hand, took a picture and set up Trumpmajority.com. Personally, I find that offensive,” Mr. Rice said at the time.

In the months following the vote, Mr. Rice has been made a pariah among those in Mr. Trump’s circle, as has his wife. “I don’t feel like I fit in with that group anymore,” Ms. Rice said on Friday, referring to the Republican base.

Mr. Trump’s efforts to sway Republican primary voters and disparage Mr. Rice have left the congressman both frustrated and puzzled. He has come to view them as a political stunt.

“Bring on the circus,” he said of Mr. Trump’s involvement in the primary. “You know, some people are afraid of clowns. I’m not afraid of clowns.”

Jonathan Martin contributed reporting.