The President's Chopper crashes over enemy's territory, he must fight his way out or be killed.

Interesting idea, but I think we've seen this movie in several incarnations. I don't see anything new about it, except the helicopter. If the helicopter crashes, it can't fight anymore, so there's no novelty. Sorry to be a downer. I like Richiev's suggestion of an aspiring VP though, but still....

In fact, in this version, the President finds out the Vice President was the one who had the plane sabotaged. It was all a plot to take power. At the end of the movie the President takes him out as well.

Not tainting, giving a time limit. Not only must the President fight his way out but he only has so much time to do it. You know, throwing another rock into the tree.