Adam Serwer and Seth Masket believe so. Matt Steinglass complicates this view:

[T]he reason why the economy is the overwhelming determinant of presidential elections is that America is a mature two-party democracy where skilled political operatives on both sides are constantly locked in a bitter struggle for advantage over the terrain of public relations. I don't think you can claim that it would have no effect on the 2012 election if Barack Obama just decided to forget about public relations and perceptions and cede the field, hoping the economy would rescue him. So I don't think political operatives are delusional to believe that the public-relations battles they fight are important to electoral outcomes.

And depressions do not always lead to incumbents' losing. Sometimes bleak economic times make people more likely to vote for what they think is the safer, less risky option. Obama certainly has used these recent kerfuffles to buttress that image as the sanest man in the room.