The logic is correct mathematically, but flawed in the real world. In the real world, you'd want to send the dollars to where it will be spent on productive pursuits. Unfortunately, governments can't do that, because the inert places, which, because of the inevitable compromises that come with a nation-state (in the US, that each state has two Senators, regardless of its population, and the Electoral College, which magnifies the effect of this) always have a disproportionate say in the national debate, will stop any attempt to target the money to the successful places. So, a large part of the government money will be wasted. On top of that, restoring confidence is the real key. What Keynes didn't realize is that the savings trap is a direct result of a loss of confidence. Restore confidence, and you get out of the savings trap. JP Morgan said it best. Asked on what basis he lent out money, he said "Character." What that means, quite simply, is that you direct your money to where you are as confident as you can be that you will make your investment back, and then some. From time to time, that confidence is lost throughout society, because of some bubble that when it bursts, causes mass privation. Restore that confidence, and you restore the economy. This is what Keynes missed, and what Obama, following Keynes, is also missing.