I was listening to this song and thought it fit the whole Sanford situation perfectly:
The meaning- I had to actually look up a good way to word this one but here it goes, from Yahoo Answers:
"In several of George Michael's songs, he used dancing as a metaphor for a relationship. A "careless whisper" could be gossip, or could be a betrayed confidence, or even a metaphor for a bigger kind of betrayal. So I'd say that he's singing about realizing that he has carelessly betrayed a lover, and now he's seeing how badly he's hurt someone he cares about. He's at the point where he realizes that he's destroyed something that matters, and there's not a thing he can do to make it better."
Kind of fits Sanford's situation in both his personal life (with his wife) and his public life (with the office of governor). And well, since Sanford met his mistress at a dance party, it seems all that much more appropriate.