I am getting in late on this one, but I have known the Clintons nearly all my life. When Bill was elected president he wore a Timex Ironman. This was to reflect his practicality and he wanted to be seen as young and vital (as a runner). Eventually his people talked him in to wearing more dress watches. The last time I saw him he was wearing a Frank Muller tank watch, this was about three years ago. He very, very much wants to be seen as young and hip, so my guess is the Panerai is an attempt at this. Probably in conjunction with Chelsea's time in Europe where Panerai is more popular.
One thing for sure, he never paid for any watch, ever. He leans on EVERYONE for favors and "gifts".