Thanks for pointing this out. I have a question though. Would he not have the sole power to order the troops home? And if does wouldn't that lead to the bases being closed due to their being empty and serving no purpose? Just curious on this point.
Yes, theoretically he could do that, but he is also obligated to do some things by treaty. Additionally, Congress has the power to persuade him through the budget such as "If you don't keep our troops in Saudi Arabia, we won't fund your 'feed the children' program" so, politically, the President could box himself into a corner by doing something others consider rash.
A President should always do as the people want him to do. So if the majority of the American people want our troops to come home than he is obliged to do so, and the consequences of it would just have to be dealt with. I know we are living in times where the will of the people is often ignored, but Ron Paul seems to be the only one that will actually put the people first.