Recessions and depressions occur when total spending--and therefore total income--is reduced. This reduction of total spending is brought on by an increase in demand for money, either to hold as savings or to use to pay down debt. Once you have your head around this, the Federal Reserve remedies for depressions and recessions--lower interest rates and higher inflation--become kind of obvious: they're both just ways to increase the supply of money, and reduce the demand for it. It also becomes obvious that government austerity exacerbates the problem; it's just one more player contributing to the reduced spending and resulting reduced income.
Obviously, there are a bunch of wrinkles in this story, but sometimes it helps to just look at the simple fundamentals of a situation. Those fundamentals indicate we should have more government spending, higher inflation, and lower interest rates. Since interest rates are already at 0, we've only got two options left.