When Ralph Norman addressed about 250 supporters at a civic center in Anderson, S.C., on Friday night, he acknowledged the biggest obstacle to his bid for the Republican Senate nomination: Donald Trump's backing of his opponent.

"Who said Donald Trump was the only one who can get a crowd?" Mr. Norman joked, referencing the thousands who gathered on the South Carolina coast where Mr. Trump rallied support for Lindsey Graham's sister, Kathy Graham, appointed last month to his late brother's seat.

Republicans will vote Tuesday in a special runoff to replace former Senator Lindsey Graham, who died last month. Mr. Norman, a hard-line conservative who backed Mr. Trump's agenda but clashed with him on spending, hopes voters reward his record and reject the president's endorsement.

"My record is my biggest asset," he said. "I'm a known quantity."

At 73, Mr. Norman is a product of South Carolina's defiant political tradition. Like Mr. Trump, he is a wealthy businessman who ran his family's real estate firm before entering politics. He supported the president's immigration crackdown and demands to end the filibuster, but did not initially endorse Mr. Trump in 2024, instead backing Nikki Haley.

His fiscal hawk stance led him to oppose Republican legislation, including Mr. Trump's signature domestic policy law. Supporters of Kathy Graham portray him as a rabble-rouser insufficiently loyal to Mr. Trump.