There has been credible production of private sector jobs in terms of numbers and I definitely agree that insistance on laying-off public sector employees, from teachers to park service employees, seems to be exacerbating the unemployment numbers, as well as leading to crowded schools, lines for services, and possibly fewer vacation options. (Some parks may be closed)
There have been recent anecdotal reports of increases in production / manufacturing jobs, human-interest stories on the nightly news about this or that (usually small) manufacturer who is hiring thirty (or two) more employees. I have, however, seen no firm numbers respecting the kinds of jobs which make up the bulk of these new private sector jobs.
The reports I have seen have also failed to say whether or not these numbers have been seasonally adjusted: we are reaching the summer, temporary employment season. Temporary jobs, related to increased agriculture, and leisure and entertainment during the summer show up around this time. As well, summer jobs in retail and fast-food or other food service, and camp / swim positions will likely be filled primarily by teen summer workers. Agricultural jobs are unlikely to make a large difference in unemployment numbers among the long-term unemployed.
Today's (Saturday's) New York Times has a very interesting article comparing the recovery following the 1970s recession with today's recovery.
NYT 5/7/2011: A Recovery Less Robust Except for the stock market, which has roared back, this recovery is much slower. This recovery shows better numbers for the stock market, durable goods, and industrial production than that of the 1970s: all signs of business recovery. Business (large corporate, in my jaundiced opinion) is recovering very well: people, not so much.
Consider two differences between the '70s and today: today, there is more automation and today, more corporations have a larger international footprint. The recovery of business does not require the recovery of people, either to perform the work or (necessarily) to buy the product. People are replaceable by machines, by transferring production somewhere else. Short sighted? Yes. But this quarter's bottom line is looking good.