I don't know what the context was in the show. I'm guessing that "figure" means "figure out."
As best I remember, the affair had some mutuality to it. It was not completely clear who seduced whom.
One normally assumes that when there is a big difference in power level, that the person with more power exploited the person with less power. In the show, was someone saying that Lewinsky was the wily predator and Bill Clinton was the baffled, naïve and innocent prey? If someone said that, then it would make sense to retort "if Clinton couldn't figure Monica Lewinsky, then he shouldn't have been president." That is, nobody can believe that someone with Clinton's experience, history of womanizing, and social intelligence, could be easily manipulated by Lewinsky.