Paradox of Thrift

'Thriftiness, while a virtue for the individual, is disastrous for an economy.’

I've noticed several articles in the past few days describing the "Paradox of Thrift". It is a construction of Keynesian economic thought: in times of recession it is in the best interest of the individual to save - however the greater economy suffers from lack of demand. This ultimately harms all individual consumers - in a form of prisoner's dilemma. The worry is that this behavior can extend the recession or even cause deflation and depression.

Keep in mind I'm not an economist, but I see several problems with this line of thought. First, it would seem that "saved" money is not (normally) hoarded away under a mattress. As long as the saved money is not held in actual bills, it is returned to the economy through banks or stocks or bonds or other investments. This increases the money supply to be loaned out to buy new things or used to create new businesses, etc.

Second, if our economy is based upon consumers spending more than they earn, it is inherently unsustainable. This would lead me to believe that our current problems will take quite some time to work themselves out. I also do not see how borrowing large amounts of more money will fix things, if the original cause of the crisis was too much cheap, easy credit. Perhaps someone can explain this to me.