Sen. Lindsey Graham (R-S.C.) won the Republican nomination for a fifth term in the U.S. Senate, securing 56.8% of the vote in the June 9 Republican primary election. The 71-year-old lawmaker died, however, on July 11 — allegedly as the result of an aortic dissection caused by arteriosclerotic cardiovascular disease.

Action must now be taken to ensure that Republicans have a champion to oppose Democrat Senate candidate Annie Andrews in the Nov. 3 general election.

'There will be time to decide.'

State law holds that in the case of a vacancy in the office of a U.S. senator from death, Gov. Henry McMaster (R) — who said in a statement that Graham "is irreplaceable" — can appoint a replacement to serve until Jan. 3 following the next succeeding general election, meaning the GOP can maintain its slight voting edge in the Senate.

Since Graham was facing re-election, there will be a special primary election to replace him on the ballot.

According to state law, the one-week filing period for this special primary election opens the second Tuesday after the death — July 21 — and the special primary election must be conducted on the second Tuesday immediately following the close of the filing period, which would land on Aug. 11.

RELATED: Lindsey Graham dead at 71

Gov. Henry McMaster (R). Kayla Bartkowski/Getty Images

"A runoff, if necessary, must be held two weeks after the first [special] primary," says state law. "The nomination must be certified not less than two weeks before the date of the general election. If the nomination is certified two weeks or more before the date of the general election, that office is to be filled at the general election."

President Donald Trump told NBC News' "Meet the Press" on Sunday that he had somebody in mind to replace Graham but declined to volunteer the name.

"I have somebody that I think would be great, but I don't want to say it now because it's just, you know, it's too soon with Lindsey," said Trump. "I don't want to even talk about anybody, but I do have somebody that I think is really good."

Sen. Tim Scott (R-S.C.) told "Meet the Press" that "there are at least one or two Congress members that I would expect Henry McMaster, our governor, to consider," but that regardless of who is named as the temporary appointment, "an open primary process would be in the best interest of South Carolinians."

In terms of contenders in such a race, Rep. Joe Wilson (R-S.C.) has made it clear that he is not game.

Wilson noted on Sunday morning that while he had spoken to Trump about Graham, he had assured the president that his "goal is to remain in the House to keep his two-vote majority for the American people."

Failed South Carolina gubernatorial candidate Nancy Mace, on the other hand, appears open to throwing her hat in the ring, telling CNN that "there will be time to decide" whether she'll consider running for the now-vacant seat.

A source familiar with the matter told CNN that Rep. Ralph Norman — a congressman once widely regarded as a possible challenger to Graham — is also "open to considering a run"; however, Norman has expressed uncertainty.

Lt. Gov. Pamela Evette is another name that has been floated in media reports as a contender. A source in her camp told NBC News that Evette received "dozens of phone calls and texts" encouraging her to jump into the race. Evette ran for governor but lost in the GOP primary runoff last month.

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