Now this is where it really falls apart. Whatever else the President of the US may or may not be, almost by definition he’s one of the best politicians in the world. His talents aren’t in punching people out—they’re in talking people into donating their pants to him. He should, just by talking and turning on his charisma, get the terrorists to offer him a date with their sister.
Wherein I see two problems.
First, best in the world? Um, no. Better than the other candidates in a US presidential election? Not necessarily, but at least that makes more sense.
Second, it doesn't matter how good your dialogue skills are if your opponent isn't interested in debating ideology with you, and would rather just empty a clip into your head. I know that the US Presidential debates are far more stage-managed these days, but no matter how much of a bear-pit they might have been in the past, by and large that wasn't one of the likely outcomes.
Jim does touch on the presidential policy posited in the film (we're the world's policeman), but doesn't go far enough. In the movie, it's not about regime change - it's about directly attacking the sovereign of a foreign power. Not the kind of thing any world leader wants to encourage.