CHARLESTON, S.C. -- In her lone debate performance, Sen. Darline Graham invoked President Trump's name about a dozen times, reminding viewers that the president had endorsed her to serve a full six-year term after the sudden death of her brother. "I trust President Trump," she said.

In their snap GOP Senate primary, Graham's two main rivals, Reps. Russell Fry and Ralph Norman, frequently point to their work with Trump: Norman notes that he spoke with the president before launching his campaign and Fry cites his partnership with the White House -- occasionally breaking into an uncanny impersonation of the president's voice.

Trump's decision to endorse Graham, the sister of the late Sen. Lindsey Graham, looms large as a field of 10 Republicans sprint toward Tuesday's GOP primary. The race is likely to pivot over whether GOP voters view Graham, who was appointed by Republican Gov. Henry McMaster to serve the final six months of her brother's term, as someone deserving of a Senate seat -- and how much sway the president maintains over his party.

Below the surface, the race is simmering with tensions. Rank-and-file Republicans are irritated that the rare Senate vacancy could be handed over to a sibling of the late senator. Allies of Graham have labeled Fry as an opportunist who could put at risk his own House seat -- if he wins the nomination, the congressman would be running for both the Senate and the House simultaneously. And some candidates view former Gov. Mark Sanford, who is also running, as a grandstander trying to rebuild his political career.

Initial polls have shown Graham with an advantage over the large field, with Fry and Norman vying for a spot in the runoff and Sanford trailing the two members of Congress. Few Republicans expect anyone to clear more than a 50% majority, which would force a two-candidate runoff on Aug. 25.

The winner will face Dr. Annie Andrews, the Democratic nominee, in November.

Graham faces skepticism within the party. GOP insiders note that her brother only received about 57% in the June primary against businessman Mark Lynch and four lesser-known candidates. Her campaign appearances have been limited because of Senate votes, and some Republicans openly question what Graham stands for.

"Giving a Senate seat out like it's a condolence card is absolutely ridiculous," said Republican state Rep. Jay Kilmartin, a Norman supporter who held an event for the congressman at a Melting Pot restaurant he owns in Columbia. "Send flowers and love and say nice things, but don't give her our Senate seat."

Graham delivered her first campaign speech at a party event last week in Lexington County, where she lives outside Columbia, and narrowly won a GOP straw poll over Fry and Norman, receiving 65 votes out of 265 cast. But she couldn't attend a Charleston GOP event Thursday because of Senate votes and fared poorly in that county's straw poll, receiving 11 votes out of 156 cast. Fry won that straw poll with 50 votes, followed by Norman with 34. Fry won a final straw poll in his congressional district Saturday.

Trump's endorsement and ties are intertwined throughout the race. Fry won a coastal district that includes Myrtle Beach in 2022 when Trump backed him in a primary against Rep. Tom Rice (R., S.C.), who voted for the president's impeachment in 2021. Fry, whose supporters chanted "fry the rice" at rallies, trounced his opponent by 26 percentage points.

Norman was first elected in a 2017 special election in his district outside Charlotte, N.C., after Trump tapped Mick Mulvaney, who had represented the House district, to serve as his first budget director. Norman has been a member of the hard-line House Freedom Caucus.

Sanford, who won a seat in Congress after his infamous extramarital affair derailed his tenure as governor, had his own Trump encounter. After Sanford was critical of Trump during his first term, the president tweeted out an endorsement of Sanford's 2018 GOP primary opponent, Katie Arrington, hours before the polls closed. Arrington won a narrow victory in the primary.

The timing of the Senate campaign is so abbreviated that the candidates have been relying on a burst of advertising, two televised debates and any endorsement that might give them an edge.

Fry and Norman have been traversing the state. Fry, who is 41, notes his humble upbringing and has cast himself as a next-generation conservative fighter focused on economic issues and high costs. Norman, who is 73 and recently placed third in the GOP primary for governor, refers to himself as the true conservative in the race with a focus on fiscal discipline.

Ahead of the primary, Fry has been on the receiving end of negative advertising by a pro-Graham super PAC called Security is Strength, which has questioned Fry's voting record and commitment to Trump, including one spot that shows Fry's face on a skillet as an AI-generated Trump flips it over in disgust.

Rep. William Timmons (R., S.C.), a Graham ally, has slammed Fry for "running for both his House seat and the open Senate seat, putting our Republican majority at risk."

As voters size her up from a distance, Graham has sought to build out a policy platform -- she has backed Trump's call for the Senate to remain in session to deal with the Save America Act, which would impose strict new voter-eligibility rules and ID requirements, and during her debate performance, she broke with her brother by supporting Trump's push to eliminate the 60-vote threshold known as the filibuster.

While Lindsey Graham devoted much of his focus to international affairs, his sister has steered her message on more domestic concerns, calling herself a "bargain shopper" who understands kitchen-table economics. "I'm not an expert on Congress. I'm an expert on the problems facing families in South Carolina," she said at a candidate event in Lexington, S.C.

Trump is holding a tele-rally for Graham Monday evening ahead of Tuesday's primary.

The primary is expected to be decided by Republican activists and insiders within the party. Nearly a half-million Republicans voted in a June 9 primary and about 320,000 GOP voters cast ballots in the runoff two weeks later. Drew McKissick, the state GOP chairman, said he anticipates lower turnout this week -- perhaps reaching as many as 200,000 voters -- because of the timing of the contest in August and the short nature of the campaign.

"I think this race is up in the air," said Gigi Bray, a Republican from Charleston who is supporting Sanford and attended Thursday's event in Charleston. "I don't think Trump had a feel for everything that was going on here."