Not Necessarily the Same Thing
Once again I'm going to be brave and state the obvious and run the risk of a "Duh" response. While my point is embarrassingly obvious, I haven't heard anyone make it during the debate on the recently passed stimulus package.
Money spent, even new money spent, on a given project or cause is much more likely to cause a diversion or reallocation of employment than to cause a net increase in employment.
As explained in my Broken Window Fallacy, when a baker has to spend money for a new window because teenagers threw a brick through the old one, he does create additional business for the window repair man, who will likely spend the proceeds on something else, and so on. The broken window does create new spending, and, perhaps, even additional employment. However, the benefits of this new spending are likely to be offset by the money not spent on something else had the window not been broken. That spending would also have led to further spending. The broken window diverted spending and reallocated the benefits, but didn't create net new spending or employment.
Substitute for the broken window the various and sundry new spending projects included in the huge stimulus package. They will result in new business for some, and perhaps even some new employment, but not necessarily any net new employment. Workers used on new projects are likely to be the same workers that would have worked on other similar projects in the same field. The workers on the new projects will be counted and added to the ranks of the newly employed; the same workers won't be subtracted from other projects because the other projects didn't materialize. As Frederic Bastiat would have put it, it's the difference between the seen and the unseen. The seen get counted; the unseen don't.
As the debt piles up, the government programs that don't get funded in the future because of the higher cost of servicing the debt won't be counted either. Those forgone programs of the future won't be counted as a cost of today's stimulus because they won't be seen either. The economy of the future will just be a little less productive and a little more sluggish than it would have been. Less will be seen in the future.