Actually, the question of whether an economic stimulus will work depends to a large degree on the perception that Keynesian economics works. The point of government as the "spender of last resort" is that the investments in the flagging economy offset the negative feedback loop inherent to recessions that perpetuate a vicious cycle, often culminating in depressions. The best example is Christmas time when the economy is doing poorly: people are less likely to buy as many gifts, or any gifts at all, even though it's precisely this lack of buying that perpetuates the bad economy. The less people buy and invest, the less they want to buy and invest, and before you know it there's economic ruin until a war or some other grand something-or-other boosts us out of the rubble pit. A stimulus uses government investment to create momentary jobs, which in turn leads to more money for otherwise out-of-work (or under-worked) individuals, which leads to increased aggregate demand through the buying of commodities and services.
Of course, if it's about defeating a negative feedback loop, which is based to a large degree on perceptions, then any, I don't know, massive ideological following against anything other than letting markets fail on their own has the potential to change what would otherwise be a positive perception toward Keynesian economics, and therefore would cause more pressure toward having a stimulus fail. We know of a few: right-wing radio and Fox News. If people are conceptually bludgeoned into believing that a stimulus won't work, then they won't be as inclined to follow the rest of the pack when government jobs open up and people have more money in their pockets that could lead to a recovery. They'll be the ones who are more inclined to save up whatever money they may have if they were government workers who got a momentary life vest and have more money during Christmas time.
It's a terrible example of a self-fulfilling prophecy. The beauty for the nay-sayers is that they can think their anti-Keynesian standing proven even though their own negative attitude may have contributed significantly to the failure of the Keynesian intervention. So much for the idea that economics and psychology are separate...
This also underscores the point that this recession has been particularly terrible and longstanding for the exact same reason the Great Depression was terrible and longstanding: lack of aggregate demand. People are making less money these days, pushed against by high costs of healthcare, education, and cost of living, and are therefore naturally unable to pull themselves out of a recession because they simply never had any money to begin with. At least in less severe recession times (after the Great Depression and before our recession) the job have-nots influenced most by their recession were boosted out by the haves, who had more spending power to pick up the slack for their unemployed neighbors.