No you didn't....You've produced the post hoc ergo propter hoc and broken window fallacies....Correlation doesn't equal causation.
By that argument, there is never any way to tell that any policy produced any change in the economy, we are operating in a total unknowable fog, and we might as well roll dice. There is also, in that case, no way to tell that the stimulus DIDN'T work, and all claims that it didn't based on results are invalid. (Actually, they're also false, as the results show it DID work. But even if they didn't, it would still be invalid.)
There are also some arguments presented above, such as "it only benefited union workers and government bureaucrats," that betray an astounding level of economic ignorance. Say a person gets hired. Say that person is a union worker. Does ONLY that union worker benefit? No: every business he spends money at that he otherwise wouldn't have had, also benefits. So does every employee of that business. So does every business that those employees spend money at that they wouldn't have had if laid off, and all their employees. Every person receiving a paycheck helps the economy. Every person without a paycheck hurts the economy.
The reason that stimulus spending works in an economic slump is because in such a slump private business has no incentive to invest. There's plenty of capital out there right now to produce a boom, but business isn't willing to invest it. Why? Because there's not enough consumer demand to justify it. If company A decides to expand and hire 100 new people, but all other companies sit on their cash, then the new products company A makes will not be bought: there won't be enough money out there in people's pockets for that to happen. And so the money will have been wasted.
Now, if ALL companies at once decide to take this risky gamble, and at the same time give everyone a raise, it will work: we will have full employment, people will spend enough money to make the investments pay off, and the economy will be out of its slump. But that won't happen spontaneously.
When we're in a bind like that, the government becomes the only agency that can invest, because it isn't concerned with making a profit. Its stimulus spending is a "loss" for the government (i.e., tends to increase the deficit), but that's all right because the government isn't a for-profit business to begin with.
But it needs to be done on the right scale. The last time we used government spending to pull us out of a depression like this (actually, even worse than this one) was in the early 1940s. It may not take quite that much, but it will certainly take more than what Obama is proposing. Still, what he's proposing is better than nothing.
EDIT: the dollar has not been "greatly inflated" over the past few years. Inflation is in fact very low. Also, GDP is measured in constant dollars, real not nominal GDP, so inflation doesn't even matter for correcting the picture.