Here’s my guess: Obama is posturing. He is throwing a bone to his base by “standing up” to the war-mongerers, and showing them who is in charge now.
After all the bluster, though, I believe that he will let them do it the way they want. Six months from now, when the newness wears off, he will quietly allow the policy to shift.
Iraq is a won war - that cannot be debated. He doesn’t want to be the one that handed Iran or AQ a victory after they faced certain defeat. Ideology means nothing to him - political expediency is everything. If giving back Iraq means political heat, he simply won’t do it.