Haley: No time in office needed to fill DeMint's seat

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Others on Haley's list include Reps. Tim Scott (R-S.C.) and Trey Gowdy (R-S.C.) as well as former South Carolina Attorney General Henry McMaster (R). Scott's name has been the one to receive the most attention.

Haley continued to play coy about a decision on Thursday, posting the lyrics to Adele's "Rumour has it" on her Facebook page without mentioning the seat.

Sources say she will pick a replacement for DeMint soon, though she has given no timeline for a choice. Whoever is chosen will be up for election in 2014, and could face a primary challenge.