I imagine that the abstraction of the reason is probably similar to the Fight Club quote about automotive recalls:
" A new car built by my company leaves somewhere traveling at 60 mph. The rear differential locks up. The car crashes and burns with everyone trapped inside. Now, should we initiate a recall? Take the number of vehicles in the field, A, multiply by the probable rate of failure, B, multiply by the average out-of-court settlement, C. A times B times C equals X. If X is less than the cost of a recall, we don't do one."
It's a similar thing with politics.
Just change A out for either people in the voting body or lobbying body, multiply by B, the probable percentage of A that you'll lose with a specific decision, then multiply by C, the amount of money (weight of a specific vote) that the specific entity would lose you.
If X is enough money/votes to win the next election, then business as usual. Of course one could say that Obama is done after this term anyway, but I have a feeling that the PTB have their best interests in favor.
edit: You've gone and deleted your post. The general gist of the question was: "What are the political forces in play causing him to change his mind about GITMO?"
