A couple that come to mind:
Deterrence (1999) - While on the 2008 election campaign trail, the sitting President, who through unusual circumstances, was not elected to his position, finds himself and several advisers stranded at a diner during a snowstorm. While he's there an international crisis takes place and he finds himself grappling with the decision of whether or not to use nuclear weapons. This political thriller doesn't entirely work, but it's certainly interesting, has some interesting twists right up until the very end of the film, and is well worth watching.
Secret Honor (1984) - Based on a one-man play, this Altman film stars Phillip Baker Hall as Richard Nixon, sitting in his office with a tape recorder and delivering a monologue about his career for a solid hour and a half. This is far more interesting than it sounds; Hall delivers an amazing performance and the script acts as a sort of fictional (one hopes) secret history of the Nixon years.
FnordChan