Appointed Sen. Darline Graham will compete in a Republican primary runoff for the party nomination for a full term, NBC News projects, though it’s not yet clear which opponent she’ll face in the one-on-one race.

The runoff raises the prospect that GOP voters could again reject a candidate endorsed by President Donald Trump.

Gov. Henry McMaster appointed Graham to fill the rest of the term of her late brother, Lindsey Graham, in July, and she is looking to also take his place on the November ballot and win a full six years in the Senate. Trump encouraged her to run and then endorsed her in a special primary that featured 10 GOP candidates, including Reps. Russell Fry and Ralph Norman and former Gov. Mark Sanford.

With more than a third of the expected vote in, Graham had about 33%, while Fry and Norman were fighting for second place with about 23% each.

The winner of the Aug. 25 runoff will face Democrat Annie Andrews, a doctor who won her party’s primary in June.

Graham, the first woman ever to represent South Carolina in the Senate, has never held elected office before. But she ran either first or second in most counties in the primary vote Tuesday night.

Still, Graham’s thin résumé appeared to cost her with some voters, calling into question the power of Trump’s imprimatur.

“I understand that she’s lost a brother and lost someone very special to her, and I sympathize with that, but at the same time, I don’t think that it’s necessary just to give it to her,” Republican voter Bob Howell told NBC News in Lexington.

Asked about Trump’s endorsing Graham, Howell said, “I like President Trump, but I don’t think that that’s necessarily what sways my vote.”