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Jenny Sanford surprising short list pick to replace Sen. Jim DeMint

(CBS News) South Carolina needs a new senator and the governor reportedly has chosen five possible candidates. Gov. Nikki Haley could make history by picking the state's first black senator or its first female senator.

One surprising name on the list is the state's former first lady, Jenny Sanford.

Sanford's turn in the national spotlight began with the personal failings of her husband, Gov. Mark Sanford, who admitted infidelity back in 2009.

What made Sanford stand apart was that she did not stand by her man -- at the press conference or in the days that followed as she was asked routinely about their future.

Sanford, referring to her husband, said at the time, "His career right now is the least of my concerns. My important job right now is our children."

Sanford divorced her husband, wrote a memoir, and spoke openly about her ordeal. But she never showed an interest in entering politics herself, which is why many were surprised this week when her name appeared on Haley's short list of possible replacements for Sen. Jim DeMint, who is vacating his seat.

Joel Sawyer, a South Carolina Republican consultant, said, "They know her as Gov. Sanford's ex-wife. They don't really know her. So in as much as people think they know Jenny Sanford, at the end of the day, politically, she's kind of a wild card."

Rep. Mick Mulvaney, R-S.C., said the short list was "really good." Asked about Jenny Sanford's name on that list, Mulvaney said, "I don't know that much about her. Of all the folks on the list, I know least about her. I don't even know about her politics."

Sanford is an accomplished professional in her own right. She worked for a Wall Street investment firm before moving to South Carolina with her then-husband, Mark. She even ran his campaigns for governor, all while raising four sons.

But when asked by a college TV station last year if she would ever run herself, Sanford said this: "I do believe it's very important for people to be involved in politics, and I think we need good people involved now more than ever. But its, actually taken a real toll on my family, obviously, for obvious reasons, so I think I'm pretty much finished with politics."

But these days Sanford has a different take, and she says South Carolina's Senate seat would be hard to turn down.

Watch Nancy Cordes' full report in the video above.