Besides the claim that it won't work, that is. We might as well see them put on the table. Edward Hugh (do read his whole post) sums one of them up:
Push to shove time has come, I fear, and if this reading is right then it is no exaggeration to say that a protracted and rigourously implemented round of QE2 in the United States could put so much pressure on the euro that the common currency would be put in danger of shattering under the pressure. Japan is already heading back into recession, as the yen is pushed to ever higher levels, and Germany, where the economy has been slowing since its June high, could easily follow Japan into recession as the fourth quarter advances.
In other words, even if the Europeans should follow suit, they either can't or won't and perhaps their loss will exceed our gain. They have a straitjacket currency union and also tougher rigidities.
The second argument is that Thailand, Brazil, and other countries are becoming bubbles. The claim is that financial institutions are still prone to seek too much risk and so the new liquidity flows to riskier markets than the U.S. The new liquidity doesn't help us much, while it becomes "hot money" for some more vulnerable countries, which in the meantime have overvalued exchange rates. The more that real rates of return fall in the U.S., the more dangerous this mechanism becomes. There is a double whammy if those same countries are betting too strongly that robust Chinese commodities demand will continue indefinitely.
I'm not trying to persuade you of these (both seem fairly speculative to me), it's simply time to take stock of the debate. It's a good example of why macroeconomic knowledge is hard to come by, namely that each situation brings some new risks and new constraints.