First of all, we must note that it is not accurate to say that the United States is currently in a recession. The US officially came out of recession (as can be seen in the bls.gov link below) in June of 2009. It is true that the US economy is not recovering very strongly, but it is also not in recession.
The more appropriate question, then, is whether the Fed is doing a good job of trying to get the economy to recover more quickly. The sad truth is that no one knows. Economists disagree vigorously on this issue and there is no way to definitively prove who is right.
On the one hand, we can argue that the economy would be doing worse if the Fed were not intervening. By keeping interest rates low and engaging in “quantitative easing,” the Fed is keeping the money supply high and allowing growth to continue even if the growth is slow. On the other hand, it can be argued that the Fed is putting too much money into the economy and is not getting any real results. Finally, there are those who argue that the Fed has done what it can but that monetary policy is not really capable of pulling us out of our slow growth.
Macroeconomics is not a precise science. Therefore, no one can really know if the Fed has been doing the right things.