Vice President Kamala Harris will travel to Columbia, S.C., on Friday to formally file President Biden’s paperwork to appear on the Democratic primary ballot in the state, according to two people familiar with her plans.

Ms. Harris’s trip will punctuate the end of a tumultuous week for her and Mr. Biden. Democrats began the week in a panic over polls that showed Mr. Biden trailing his likely Republican challenger, former President Donald J. Trump, in five of six expected battleground states. Then they found their spirits lifted when Democrats performed well in Tuesday’s elections in Virginia, Kentucky and Ohio, where a ballot measure enshrining abortion rights in the state constitution passed.

The Biden campaign had said its South Carolina paperwork would be filed by Representative James Clyburn, the South Carolina Democrat who helped resuscitate Mr. Biden’s 2020 campaign by endorsing him three days before his state’s primary. Mr. Biden repaid the favor by pushing the Democratic National Committee to put South Carolina at the front of the party’s presidential nominating calendar.

Ms. Harris and Mr. Clyburn will meet to file the primary paperwork at the South Carolina Democratic Party headquarters, said the people familiar with the plans, who spoke on the condition of anonymity because the trip was supposed to be a surprise.

After The New York Times asked about the trip on Thursday evening, Ms. Harris made a sly suggestion on social media that she may appear with Mr. Clyburn.

The White House had intended to keep Ms. Harris’s trip secret until she arrived in South Carolina. Her official White House schedule for Friday reads: “The vice president is in Washington, D.C., and has no public events scheduled.”

A Biden campaign spokesman and Ms. Harris’s White House spokeswoman declined to comment on the trip.

Mr. Biden, at a fund-raising event Thursday night in Chicago, dismissed polls from The Times and CNN released this week that each showed him trailing Mr. Trump.

“The press has been talking about two polls,” Mr. Biden said. “There are 10 other polls we’re winning.” Mr. Biden then told the assembled donors that their money was not wasted on him but joked that he could “screw up” during his re-election bid.

Representative Dean Phillips of Minnesota and Marianne Williamson, the self-help author who ran in the 2020 Democratic presidential primary, have already filed paperwork to appear on South Carolina’s Democratic primary ballot.

Nevada, the second state on the party’s calendar, had its deadline to file for the primary last month. Mr. Biden, Ms. Williamson and 11 other candidates filed to run in Nevada’s Democratic primary.

Mr. Biden did not file for the primary in New Hampshire after officials there refused the D.N.C.’s request to move its primary after South Carolina’s.

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