Darline Graham in serious talks about running for late brother Lindsey Graham's Senate seat

Senator Darline Graham is actively considering a run for the U.S. Senate seat previously held by her brother, Lindsey Graham. She is reportedly in serious discussions about entering the Republican primary scheduled for August 11.

Graham was appointed by South Carolina Governor Henry McMaster to serve out the remainder of her brother's current term, which concludes in January. She was sworn in on Tuesday, becoming the first woman to represent South Carolina in the Senate. Her appointment followed the sudden death of Senator Lindsey Graham last weekend.

Sources familiar with her plans confirmed to CBS News that she is weighing a bid for the seat. While Darline Graham has a background in disability services, including her most recent role as commissioner of the South Carolina Commission for the Blind, she does not have prior experience in elected office.

Despite her lack of political experience, her colleague, Senator Tim Scott, who also chairs the National Republican Senatorial Committee, appeared optimistic about her prospects. "Darline has so far been off to a remarkable start," Scott told CBS News. "Why not her?" Lindsey Graham had served in the Senate since 2003 and was widely expected to seek re-election in November.

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Darline has so far been off to a remarkable start. Why not her?