No. Unemployment does not reflect the actual number of people employed or not. The definition of unemployment is the percentage of people who do not have work, and ARE LOOKING for work. Therefore, both jobs AND unemployment can rise at the same time. For instance, a homeless guy who has never put in a resume is not considered 'unemployed', he is without employment though.
SO, what the economist is saying is that more people are looking for work, which means that the hopelessness of the American recession seems to be subsiding and they have probably started looking because jobs are starting to open up.
I did not comment on this earlier because the original post did not make sense since the article was very straight forward, but I guess the definition of unemployment is easily misunderstood at times.
Spaniard, you have some good points, although I think they are not accurate with the information given in the article. As I mentioned above, it does not necessarily mean that employers are shedding jobs. Furthermore, yes, jobs are difficult to come by at times, but I have faith in a market economy.
[You guys should all move to western canada. Although we too have had a slight set back due to your recession, we got lots of great paying jobs still!]