President Trump wants South Carolina Sen. Lindsey Graham's sister to fill his seat on an interim basis after his unexpected death early Sunday.Why it matters: Trump has a close friendship and working relationship with South Carolina Gov. Henry McMaster (R), who's expected to make the temporary appointment today.Before Trump's announcement that he favors Darline Graham Nordone to serve her brother's term the rest of the year, Trump's advisers were sending signaling that Graham Nordone likely would be the pick.South Carolina will hold a GOP primary on Aug. 11 to pick a new Republican nominee for the Senate. The winner of the Nov. 3 election will take over Graham's old seat in January. Zoom in: Graham's unexpected death made the GOP's Senate margin even slimmer now, increasing the pressure to fill the seat as soon as possible.Picking a "placeholder" like Graham's sister gives the governor and president time to decide whom to support during the primary election."This would be a fabulous tribute to Lindsey, who loved her dearly!" Trump wrote Monday on Truth Social, underscoring his friendship with Graham."McMaster listens to Trump and Trump listens to McMaster," a senior Trump adviser said.Inside the room: South Carolina Rep. Russell Fry (R) is a favorite candidate of some Trump insiders, who say he has good fundraising potential and a safe Republican seat that won't hurt the GOP's House margins.Fry's colleague, Rep. Joe Wilson, has also surfaced as a possible candidate. He's the father of South Carolina Attorney General Alan Wilson, the GOP's nominee for governor.The intrigue: Rep. Nancy Mace, who came in fifth in the GOP gubernatorial primary, has drawn an exceedingly negative reaction from Trump's political operation by appearing to float her own name on social media to replace Graham the morning his death was announced, two sources told Axios."If Mace ends up in a runoff, we'll drop $2 million on her head to keep her out," said one top official with Trump's political operation. "All we want is a Republican who is sane and can work with the White House.Said a second: "POTUS wasn't a fan already, but putting herself out as a candidate while everyone was absorbing the news of Lindsey's death was in poor taste, even for Mace."What they're saying: Mace told Axios she was being unfairly singled out, noting that Graham's former primary opponent, Mark Lynch, and Republican Rep. Ralph Norman also had floated their names."Two men announced they were running to replace Lindsey Graham yesterday — within hours of his passing. I wasn't one of them," Mace said."The pearl clutching by people afraid I will run hit a new high," she added.