The first set of "real" numbers of jobs "created" by the so-called stimulus program were released on Thursday, and they say that the federal government's spending has "created or saved" 30,000 jobs to date. The number is, in my opinion, fraudulent.
The numbers rely on self-reports from the companies and agencies recieving federal contract money, but there is no way these data can be verified. Even if a firm were to lay someone off, for example, there is no guarantee that the person wouldn't pick up a job somewhere else in the economy. Moreover, most of the jobs "created" or "saved" have been in the Washington, D.C. area which--surprise--has hardly felt the effects of the recession.
In addition, quantitatively distinguishing between a job "saved" or a job "created" if practically impossible. Economist Greg Mankiw has a good summary of the problem and more accurately characterizes it as an act of "political genius."
The total estimates of jobs saved and created used to justify the stimulus package rely on "inferences", not direct counts. These estimates are based on asssumptions about job growth (or loss) trends. An outline of the methdology from the White House Council of Economic Advisors can be found here. See also CEA chair Christina Romer's Q&A on the issue here.
Of course, the number itself is misleading. The 30,000 "jobs" are those directly related to government contracts. It assumes that none of those jobs would exist anywhere in the economy without federal spending or the government contract. Yet, the economy isn't dead. It may be going through a rough patch, but unemployment has yet to hit 10 percent.
In addition, for economists, the term "jobs created" almost always refers to estimates based on net jobs (jobs gained minus jobs lost). The estimates of jobs created and saved are simply based on the reporting from contractors, not any real calculation of net jobs in the economy.