You need to widen the perspective beyond the US to grasp the rationale, as Obama is but the most prominent dancer in the global western ballet around Syria but it's not a solo show. It's not Obama on his own that painted himself into a corner (though it's quite fair his political opponents are depicting him that way), but all the NATO allies are in the same bad spot. Beside, they've not really painted themselves into a corner so much as they've long all been stuck in a diplomatic deadlock with Russia over Syria, and now Assad is making all of them look bad and they have to wither this without crossing a no-return line and they're not quite sure yet where that line is. They all barked loud their outrage with one voice, now they're letting supposed "hesitations" and "divisions" among NATO allies show and they let Russia its chance to bark back, which all serve to justify moving slowly. Typically the US will voice "frustration" at the UN and play the bad cop to add pressure, and others' job will be to dither so the US doesn't get a consensus for a strike within NATO unless it really wants one, not just pretend it intends to act. Meanwhile Russia is stalling, trying to delay as long as possible having to veto a resolution that would permit the use of force against Syria. Right now Turkey pushes for a strike, France is saying everything and its opposite in turn - the only consensus being to "firmly condemn Assad", the UK voices caution and its desire to wait for the results of the UN investigation, Canada announced it will support the US and NATO if they strike, even without a UN mandate, but it can't participate militarily, etc.

It's a well orchestrated diplomatic ballet, hot and cold and quite typical of this sort of situations (but that we hadn't seen that much of since the cold war). In the end NATO allies won't strike without a UN mandate unless it has sufficient assurances Russia is ready to stand aside or will react diplomatically only, which apparently they won't have (ATM a strike on Syria would be a major loss of face for Russia). And whatever they say, they're all waiting to see first to see what will come out of the Security Council. The "imminent" limited strike idea was of course mostly a show for the gallery.