Martin Wolf invokes an interesting counter-factual:

Suppose that the US presidential election of 1932 had, in fact, taken place in 1930, at an early stage in the Great Depression. Suppose, too, that Franklin Delano Roosevelt had won then, though not by the landslide of 1932. How different subsequent events might have been. The president might have watched helplessly as output and employment collapsed. The decades of Democratic dominance might not have happened.

I think that's correct. It's also a useful lesson for liberal who compare President Obama with President Roosevelt. The latter's political success owed an enormous debt to the fact that he took power after the economy had hit bottom and begun to rebound. Indeed, Obama's situation is more like an election that took place in 1929, leaving him to take the oath of office in early 1930, just as the bottom was falling out.

Wolf proceeds to lacerate Obama for failing to act boldly in response to the crisis:

But this time was different: the crisis brought Barack Obama to power close to the beginning of the economic collapse. I (among others) then argued that policy needed to be hugely aggressive. Alas, it was not. I noted on February 4 2009, at the beginning of the new presidency: “Instead of an overwhelming fiscal stimulus, what is emerging is too small, too wasteful and too ill-focused.” A week later, I asked: “Has Barack Obama’s presidency already failed? In normal times, this would be a ludicrous question. But these are not normal times. They are times of great danger. Today, the new US administration can disown responsibility for its inheritance; tomorrow, it will own it. Today, it can offer solutions; tomorrow it will have become the problem. Today, it is in control of events; tomorrow, events will take control of it. Doing too little is now far riskier than doing too much.” This was right.
The direction of policy was not wrong: policymakers – though not all economists – had learnt a great deal from the 1930s. Sensible people knew that aggressive monetary and fiscal expansion was needed, together with reconstruction of the financial sector.
But, as Larry Summers, Mr Obama’s chief economic adviser, had said: “When markets overshoot, policymakers must overshoot too”. Unfortunately, the administration failed to follow his excellent advice. This has allowed opponents to claim that policy has been ineffective when it has merely been inadequate.

This is a more arguable point. I have some more thoughts on this debate in my forthcoming TRB column. The short answer: It's highly debateable whether Obama could have gotten a larger stimulus through the Senate.