Have a laugh while you watch.
http://thedailyshow.cc.com/videos/q7hzaa/the-big-bank-theory
The debt wasn't issued for the purposes of QE. It would have been issued regardless, so don't make up silly statements about how every dollar pumped into the economy is linked to new debt. We created dollars to buy the debt which would have been bought by others. The debt has nothing to do with it at all. The QE just simply bought debt. It also bought MBS. That wasn't government issued debt.
As for keeping rates down, sure it did a good job of that - and killed savers, forcing everyone to move into higher risk assets (which they will get burned on down the road - tomorrow, or next week or next year). They inflated a housing bubble (again) and this time an all-asset bubble as well. And all for what? So a few people who would have lost their house because they bought too big a house at stupid rates could refinance? You must be joking.
Now the Fed is frantic because rates aren't rising despite QE ending, and it's because they've gobbled up the bond market, and there's no liquidity out there! How ironic, thwarted by their own stupid policy.