Of all the things I've heard said about GWB, timid responses were not among them. I doubt anyone considered him overly cautious. He certainly believed in American military adventurism.
However, the basis of Obama's foreign policy seems to be that if it doesn't directly affect American interests, or American citizens, he really doesn't want to interfere too much. These people are essentially forcing him to address people getting murdered specifically because they are American. They are making it his business.
I'm not moved by it. If someone comes to the US, kills a journalist on our soil, films it, posts it, then leaves, we have a problem. But in this case, I can't help but see this as an occupational hazard. This is to say, I don't think it is reasonable to expect US foreign policy to be built around the idea that anyone with an American passport can traipse around the globe and dig into the most awful places, reporting on the most awful people and events, and whoever messes with said passport-holder, that's who we go to war with.
And you are atypical. This sort of thing has an impact on the president, even though I generally agree with the policy of moving away from military adventurism when at all rational. I may not like it, but it's also reality. The US isn't ready yet to take a less aggressive world view.