The New York Times reports that "some school districts said that they might not have actually laid off teachers without the stimulus money." The Times is too polite to add that the rest -- the ones that claim they're sure these jobs would have been cut but for the federal money -- are lying. In the face of uncertainty, recipients of federal money aimed at boosting employment have a powerful incentive to err on the side of reporting more jobs rather than fewer.
Even if recipients are honest, diligent and psychic, the jobs they report are not, strictly speaking, jobs. Instead, they are "full-time equivalents": the number of hours in a quarter for which employees are paid with Recovery Act money, divided by a full three months of work. This calculation invites recipients to inflate their numbers by counting all hours on stimulus-funded projects, instead of just the hours worked by people who otherwise would have been unemployed.
Even when done correctly, the quarter-by-quarter accounting exaggerates the number of "direct jobs" linked to stimulus spending. When President Obama promised the stimulus would produce 3.5 million jobs, most Americans did not imagine he was talking about three-month gigs.
But the most fundamental flaw in the president's stimulus hype is the notion that more jobs are always better (which also underlies his claim that global warming will be a boon to the economy as long as we spend lots of money to mitigate it). According to this standard, if the government really did find a supplier who spends 520 man-hours to deliver one pair of work boots, it should buy as many as possible.