New Delhi, Aug. 10 -- COLUMBIA, S.C. - South Carolina Republicans will vote Tuesday in a special primary that tests whether a Trump endorsement carries more weight than a congressman's months of statewide name recognition.

Darline Graham Nordone, the interim senator filling her late brother's seat since July, and Rep. Ralph Norman, who built a statewide profile through his gubernatorial run earlier this year, are the two principal candidates competing for the right to hold the seat through January and to enter any future general election with an incumbent's advantage in a state that has not sent a Democrat to the Senate in decades.

The stakes extend beyond South Carolina. A Graham win would validate Trump's approach of endorsing candida...