I don't think very much of patriotism (I think it is misguided loyalty) and I don't think much of patriotic movies. I don't like to think in terms of black and white and I particularly think it is dangerous when whole countries start thinking like this (as I read the history of the world wars, I'm convinced this is one of the primary reasons why these wars occurred). Thirteen Days is based on the Cuban Missile Crisis, a time when we clearly thought in terms of us (Americans) vs. them (the Soviets), but the movie itself focuses on an internal American conflict which highlights the grayness in such situations.
The conflict depicted in the movie is over what action to take when Soviet Premier Nikita Khrushchev places a few nuclear missiles in Cuba, less than a hundred miles from Florida and with the potential to result in the death of twice as many million people if a wrong decision is made. The parties at odds with each other are President John F. Kennedy (Bruce Greenwood) and his close advisors, and the military establishment. The latter are more prone to think in black and white terms than JFK and look for any excuse to attack the Soviets. JFK, who is considered a wimp, looks for options that would not start the first nuclear war. In the end, it is Adlai Stevenson (Michael Fairman) who saves the day by facing down his counterpart at the U.N.
Bruce Greenwood makes for nice President. (He should consider running someday.) Kevin Costner as Kenny O'Donnell, Kennedy's confidant, is decent. The movie doesn't really revolve around him that much, but it is his perspective that is emphasised most. Stephen Culp is also a convincing Robert Kennedy. In fact, all the actors do a great job playing their characters, which makes this movie work really well.
In a film like this, where we already know the outcome, it takes some effort to keep the suspense level high. Director Roger Donaldson does this by showcasing the petty politics that happens in such tense situations and the back-door deals that have to be made (sometimes at the cost of people's lives) to appease a few egos.
Which brings me to my final point: the Soviets did blink (at least temporarily, since a compromise was reached) and a nuclear war was averted. Everyone knows we came so close. But everyone should also realise that whether or not a war occurred really depended on a few egos who ended up being responsible for the fate of millions of lives. And that still hasn't changed.