It is estimated that that the US has some 700 to 800 bases and 250,000 soldiers outside the US. A good book about they work is Robert Kaplan's book "Imperial Grunts: The American Military On The Ground".
Despite Obama's rhetoric the expansion of the US presence around the world is going on. The newest goal seems to be encirclement of China , but the encirclement of Russia is going on too. Of course it is not Obama alone. He is under serious pressure from the increasingly extremist views in the Republican party.
The problematic aspect of this is that nearly every country in the world is put for the choice whether it is for or against the US. Being for the US implies accepting US bases, military training and often some symbolic participation in Afghanistan. I find this disturbing and destabilizing.