I agree with what you're saying, it was a mistake for Obama to come out with the answers before all the information was in, but people do demand answers immediately and it wouldn't look good to many people to delay those answers. Many people have an unrealistic expectation for how fast these processes are, of course each one is unique in itself. For example you have a completely unrealistic understanding of how fast reinforcements can move around the world, a few hours is not enough time unless something is already in the nearby area and is already equipped for quick reaction and small team operations.
There were teams ready in Southern Italy, and could of been on site in Benghazi in less than one hour.
Here's the problem you are having. You assume the White House, the CIA, and the State Department had no idea what caused this attack, for at least 2 days.
We now know that is not true. There is quite a bit of intelligence that we now know came in real time, that pointed to Ansar al Sharia. From the beginning, the State Department reports all included language about a coordinated terrorist attack. None of the State Department reports mention a protest, or a video.
So, think about this. Try not to be partisan here. Intel was coming in real time that suggested terrorism. Within 2 hours, Ansar al Sharia is claiming responsibility. We know that the State Department took that claim seriously, because they issued a warning to "Embassy Tripoli". THERE'S your proof. They knew who was responsible, so they issued a warning to the embassy in Tripoli. That's simply a fact. We know this now.
It's not a mistake to give quick statements about the attacks. They simply could have said, "intel is coming in, and we don't know at this moment who exactly is responsible". That would have settled it. But that's not what the administration did. They emphatically stated that NO EVIDENCE was available that supported the idea of a premeditated attack. Jay Carney said it, and Susan Rice repeated it over and over again. They blamed the video. They claimed to have HAD the reason for the attacks, which was an out of control protest over the muhammed video. They gave a specific reason, and it turned out to be completely untrue.
So, you must conclude that either A) They are covering the whole thing up, or B) They are simply so incompetant, that they don't understand how to say "we don't know yet" as opposed to advancing a false narrative.
Either they are covering up, or they are completely incompetant on how to handle a crisis situation. I know what I believe, because I continue to research what happened. IMO, they lied their asses off, and hoped this would be a non story until after election.