I don't know. Economic models do not, in my view, qualify as successful scientific theories. They do, however, shed a bit of light on matters of public policy from time to time (some more than others). The perspective I offer on this question is one that I find persuasive, supported by what I think to be the most compelling models, but I hardly consider it the final word on the subject. So, take from it what you will.
The standard framework, in contemporary business cycle theory, for thinking about recessions is provided by the New Keynesian DSGE family of models. These models pin the blame for recessions upon insufficient aggregate demand (AD) for goods and services produced by the economy. Sticky prices (prices that change too slowly), in the face of negative AD shocks, cause the economy to produce less than it is capable of, rendering some fraction of the economy's basic inputs (land, labor, capital, etc.) idle. Given price stickiness, the recipe for greater utilization of the economy's capacity, which would increase output and employment, is more AD.
Even if this is the best way to think about most recessions, one may always suppose that this time was different, that this was a fundamentally different kind of recession. The evidence, however, suggests otherwise. Nominal gross domestic product (NGDP) measures the aggregate level of money expenditures. It is, therefore, the statistic that most closely tracks AD. During the postwar period, variation in NGDP growth explains about 2/3rds of the variation in output growth. Variation in output growth, in turn, explains about 3/4ths of the variation in unemployment. These figures increase, not decrease, when we restrict the data to the most recent recession (plus the subsequent recovery). In other words, this time looks to have been no different from a run-of-the-mill recession--just a very deep one, precipitated by a steep decline in NGDP. While the housing crisis, or the financial crisis, may have done something to NGDP, the economic plunge did not begin when the housing market started to collapse, nor when the shadow banking system suffered a run; it began when NGDP went south (before the demise of Lehman).
To me, therefore, it seems the focus of our inquiry should be on AD. Did Obama's policies (not only those he implemented, but also those he pursued aggressively) stimulate AD relative to what would have otherwise occurred? And to the extent that they did, were there other ways to stimulate AD that would have had fewer negative side effects? These are the questions we ought to be asking, in my view. There is much to economic policy besides AD, of course, but Obama's impact on the recovery from recession is almost entirely a story about AD. My next post will be about whether Obama could've done more to boost AD, and whether his efforts to date have been successful.