The stock prices goal is not my read on it.
Most assets are compared (financial calculations) against the riskless asset (very short treasury is the proxy). So the risk reward trade-off changes which might cause stocks to go up.... "Take the risk for better return". Of course there is speculation around it and the hopes of big gains due to a turn around.
What I read was the QE 2 is to try to grow the economy by making money cheap to borrow.... but the underlying political goal is the hope it will in turn turn around unemployment... which in turn is needed to drive the economy up (consumers buy).
The problem is it is that money is already cheap and cannot get much cheaper.
Some seem to believe that QE 2 will not fix unemployment (in the near term)... they believe we are experiencing a structural realignment (in labor)... The bubble created an artificial demand for certain jobs... those jobs may come back sometime in the future, but it will be awhile. Plus, many of those people cannot shift into the job demand that is available (and will grow), because it requires training which takes time and effort (e.g., health care and technology).
At this point, no one really knows!
While I have optimism that America can pull out of this... the question is; Will it work and how long will it take! Will we stagnate and/or slide into another recession?