The most likely explanation is that Obama thought, while the attack was happening, that it might really be an angry protest about an offense to Muslim sensibilities; and he shrank from using the US military to hit back at offended Muslims. In effect that would have been “being at war with Islam;” the very last thing he wants.
If indeed it had turned out to be offended Muslims, there’d have been similar attacks all over the world, not two months before the election. Somebody somewhere would have died, possibly somebody of high profile. Obama’s Arab Spring would have been reset to Fall.
In other words a 100% political decision. What’s good for Obama.
Perhaps the next story will be they thought it was a wedding celebration? Let’s hope Romney asks him when he found out it was a military attack? Was it before or after the UN address?