CNN reports on Commander in Chief, a game that lets you play the President. The title appears to actually bear the title Geo-Political SImulator 2009, and has been around at least since 2008, although I didn't know about it.

The developer describes the game as "an extremely thorough and realistic simulation of the planet, at all levels: politics, the economy, environment, the military, science, culture, religion..."

A trailer on the developer's website seems to depict a choice-based simulation game, but footage of army units may also suggest that it includes some RTS-like elements. I guess we'll have to try it and see.