He will you need have no doubt. However he will not leave. He will stay and atay and stay.
Haiti is not a place where success stories are easily made. It has quagmire written all over it - Obama’s quagmire.
This could easily become an unwelcome & costly distraction from his domestic agenda. I doubt he wants that.
He will turn over responsibility to the UN at first opportunity, to the detriment of the Haitians. The difficulty is that if he hands over to the UN when things are still chaotic, he looks like he failed. But the longer he waits, the more burdensome it becomes.
Remember, the UN was there long before the earthquake. It was a shiite hole then & it will just be a worse shiite hole now.
For the immediate future though, Haiti is his to screw up.