Most graceful exit strategy: The UN Security Council
If I were President Obama, I would pivot hard toward relying on the UN Security Council to resolve the terrible chemical weapons crisis in Syria. We will do everything we can to convince them, but will not "go it alone."
This has several attractive features.
* It would mean there would be no air-strikes, but the blame would be on Russia and China vetoing them.
* The UK would probably vote with us, knowing it would be vetoed. (The Parliament vote is not binding. I imagine Cameron would be happy to join us in a vote known to be merely symbolic.)
* France would probably vote with us. Even if France gets pieds froid (sp?) a meaningless vote would allow her to also save some face.
* Heck, maybe we might wheedle (aka 'buy') enough support from the current non-veto-power Council members to get a 8-7 vote "win" with Russia and China vetoing, or even a 6-5 "win" with Russia vetoing and China and others abstaining.
As ways to get out from under an increasingly unpopular scenario go, that seems the most face-saving route. Even as mere theatre, there would be an action (on TV!) by someone other than Obama that represented "the decision."