The Obama administration deserves credit in trying to make the spending from the stimulus package and its impact on employment as transparent as possible. They asked the beneficiaries of this money at the state and local level (both Democrats and Republicans) to list the jobs funded with it.
This is a great step forward in government transparency and the Obama administration deserves credit for it, whether or not someone agrees with the stimulus. (Stimulus opponents should be able to go through this list and pick out stupid projects and point out how some large number of people wasted their time doing useless tasks.)
Given that the purpose of this effort has been to simply convey information (which the Obama administration expected to show it in a favorable light) it is remarkable how critically this effort has been treated in the media. There have been numerous articles highlighting the errors in reporting. This was pretty much inevitable, given that they were relying on tens of thousands of public officials, many of whom had little interest in being careful in their reporting of jobs.
More recently, the media are implying that there is something illicit in the switch from "jobs created or saved" to jobs funded by the stimulus. The NYT called this a "new, more expansive definition," as though the Obama administration was just trying to cook the books to produce bigger numbers.
In fact, this is about the most straightforward way to measure jobs imaginable. There is no perfect way to construct the counter-factual of what the world would look like without the stimulus, but reporting the number of jobs funded through the stimulus is at least a relatively objective measure of its impact.