Troublingly, this is the exact opposite of what is needed to get out of a recession. In order to increase employment and restore growth, spending needs to increase, not decrease. If consumer spending is at an all-time low, why would corporations hire more people, instead of less? This is where Keynes came in. He argued that, unlike corporations, the government wasn't limited by the temperamental swings of the market. In fact, the government had the ability to do what very few corporations can: go into a very large amount of short term debt. The idea behind this is to commission large projects which force corporations to rehire and increase expenditures. As such, employment increases and salary for those employees does as well. Once consumers have a sufficient amount of disposable income, the other sections of the economy are revitalized as well.
There are a couple easy pitfalls with this, though. First is the debt aspect -- if you choose the wrong projects to invest in, then the government may end up in permanent debt. Consider two projects: one requires high capital investment, but it will spur greater economic growth and profits in the long run. The second also requires high capital investment, employs a lot of people, but it's essentially a one-time product. A great example of the first is infrastructure projects like the Tennessee Valley Authority. It cost a huge amount to build, but it also provided cheap electricity to the area, generating revenue, and also provided a great place for businesses to relocate to (because of the cheap electricity) and increased employment and income rates of almost everyone in the area. An example of the latter would be something like an advanced jet fighter (with no war going on). The problem is that once built, the jet fighter is essentially done. A high capital investment produced a short term investment, but it generally has a low rate of return. Of course, the reason why this worked in WWII is fairly simple: we were the world's bankers and manufacturers.
Therefore, the problem thus far has been crippled because it is essentially half-hearted. Stimulus spending, to be effective, must be a large proportion of the country's GDP (around 4%). In contrast, $3.27 trillion is about 2.1% of our ~$15 trillion GDP[1]. For a more accurate (but still back of the napkin) calculation, Krugman wrote this in January of this year[2]. I believe that Krugman also overlooks many of the problems with the spending projects themselves: to be effective in the long run stimulus spending should be focused towards long term improvement projects. Infrastructure development is a great example of that, but so are things like alternative energy and scientific R&D. Too much money I think is spent on things like super-high performance military jets. While this satisfies the short term criteria, F/A 18E/F Super Hornets probably don't increase consumer spending as much as equivalent infrastructure spending over 10 years.
That said, I still agree with Keynes and most modern economists that stimulus spending is probably the best way the government has to help the economy. It's not a magic bullet, but we do have a sizable amount of historic evidence in favor of stimulus spending and against other things. (Consider that Keynes's theory of economics did not come about until the late 19th-early 20th century. Prior to that, government did not go into debt. As a result of that and lack of regulation, recessions were harsher, more frequent, and lasted longer.) Of course, macroeconomics is mostly guesswork, mingled with shreds of enlightenment that don't add up to all that much anyway.
[1] http://blog.heritage.org/2009/02/12/true-cost-of-stimulus-32... Really, this is a pretty generous calculation anyway, considering that this is over 10 years and some of the stimulus will probably come back in taxes. [2] http://krugman.blogs.nytimes.com/2009/01/06/stimulus-arithme...