Walter Jones has the details on the possibility:
“Senate Health Committee Chairwoman Renee Unterman, R-Buford, is lobbying for her chance. In a two-page letter to the leadership obtained by Morris News Service she lists her loyalty, competency and social skills. She also notes that Republicans could benefit by putting more women in leadership roles.”
Bonus: A quote from consultant Mark Rountree, who posts here infrequently. Go read the whole thing.