Continuing the policy of trying to divide and conquer your political opposition, the president chose a Republican to steer the Department of Defense - a department he cares very little for. But in doing so, he has managed to choose a Republican who has some shaky positions on foreign affairs that happen to align with the president, and ones that will not rest well with those in his own party.
By selecting Chuck Hagel the president is daring Republican to reject his nominee. They either give him an ally on Israel and let him look bi-partisan or they reject him in look intransigent and stubbornly, blindly opposed to all that is Obama-driven to the point of being unreasonable and self-destructive in the eyes of the media, and therefore casual observers.
Well played, albeit cynical and destructive, Mr. President.