They did provide military back-up. They sent Delta Force commandos from Fort Bragg to Sicily, but they didn't arrive in Benghazi in time. The battle fought at the consulate was not a continuous one. It was two, punctuated attacks, with a long pause in between. This
article offers other reasons for the slow response that make it clear that President Obama did everything he could. I don't think it's an exhaustive investigation by any means, but there are clearly other reasons for the lack of security.