I'm not saying Keynes (or Obama or Larry Summers) is wrong because all spending does is bid up prices and wages. I'm not trying to prove that the stimulus failed. I'm challenging the standard macro textbook story that says aggregate demand leads to output that leads to employment.
I do not think of jobs as being created by aggregate demand. I do not think of jobs as being created by firms.
Market activity consists of patterns of specialization and trade. Two hundred years ago, a lot of people produced stuff that they could sell pretty directly. A farmer could sell unprocessed food in the nearby village. A tailor made clothes. A blacksmith forged horseshoes. A doctor billed a patient directly.
In a modern economy, these patterns are incredibly complex and indirect (or roundabout, as the Austrians would say). Today, many people have jobs that yield nothing that a consumer would buy directly: Logistics expert. Database administrator. Corporate event planner. Training co-ordinator. Media relations person.
How does one of these modern-era jobs get created? You might say that it gets created when an entrepreneur tries out a new method of satisfying some need in an efficient way. But the satisfaction and the efficiency are highly context-sensitive. Shake the kaleidoscope, change the pattern, and the satisfaction and efficiency disappear.
You do not fill the typical middle management position by picking up somebody hanging out in a parking lot. Modern jobs require substantial human capital investments on the part of both workers and firms. From this, it follows that patterns of specialization and trade need to be stable and well established in order for jobs to be created.
If you are going to speculate on developing part of a new indirect pattern of specialization and trade, you need to be able to extrapolate from the current economic environment to the future. How do you do that right now in industries like health care and financial services, where most of the specific regulations envisioned in the recently-passed legislation are "to be determined"? How do you do that on the basis of "stimulus funds" that are temporarily reshaping the opportunities for profit and loss in the economy?
I do not know how one can possibly determine the effect of the stimulus on jobs. The jobs that the CEA and the CBO say are created are nothing but figments of some model's imagination. Counting workers hired by some particular subset of firms is a mindless exercise. When it comes to the creation and destruction of patterns of specialization and trade, the process is very difficult to monitor and causality is very difficult to trace.
[UPDATE: See Greg Mankiw on the long duration of unemployment, and see Mark Thoma citing David Altig on the relatively high number of job vacancies relative to unemployment. I would explain both of those phenomena as being due to destruction of human capital. Under the 2007 pattern of specialization and trade, some workers had human capital which suddenly depreciated. It is difficult to create a new pattern.]