The more I think about it, the more I believe that President Obama can't -- in a political sense -- demand an investigation into torture. He needs to appear as if he's above what is clearly going to be defined as a partisan attack (as wrong as that is).
That's not to say there shouldn't be an investigation -- there absolutely should be. But the president doesn't need to take the lead on it. In fact, it's totally unnecessary in a legal and a constitutional sense. Ultimately, there's no harm in the president staying above it all. Justice could still be served and he could continue to focus on his agenda.
Concurrently, if Congress or Justice or both decide to investigate, the president could actually use up just as much political capital trying to stop the investigations as he would have trying to actively push for it.
So methinks the president will publicly oppose an investigation, but he won't make any effort to stop it.
Adding... In a perfect world, it really has to be Holder appointing a special prosecutor. Not Congress. Congress will make it look like partisan revenge -- too much politics. And if it's the House, it'll look like a carnival sideshow on top of it all.