I'm too lazy (or perhaps too disinterested) to do the research, but I bet if someone were to take a good look at presidential approval ratings over time, he would find something close to a direct correlation between approval ratings and the relative state of the economy. There would probably be a few aberrations mixed in, due to things like unpopular wars, publicized extramarital affairs, etc., but I would be surprised if such a trend weren't generally apparent. We Americans love our money, and when we have less, we tend to get cranky.
To be sure, Obama made a lot of promises during his campaign that anybody who truly understands the way our government works should have realized were far too lofty to ever be fulfilled. He told us what the majority of Americans wanted to hear, which seems to be a good idea when trying to get elected. In that regard, he is really no different from any of his predecessors.
Overall, I think Americans have a grossly exaggerated view of how much influence a president actually has over the state of the union. Lest we forget, while a president can propose change, only Congress (whose approval rating is lower than Obama's BTW) can enact it. I agree that Obama has shown weakness in his dealings with Congress, and I have found that disappointing, but realistically, I question how much good it would have done him to try and bully them.
It is my belief that poor economic conditions and the hard times that come with them are much less indicators of individual incompetence than of inevitable systemic failures. In time, the system will be corrected, one way or another, and I suspect the guy or gal sitting in the White House when that starts to happen will enjoy heroic approval ratings.