I think the answer is "yes"...
David Altig of the Federal Reserve Bank of Atlanta http://macroblog.typepad.com/macroblog/2010/07/a-curious-unemployment-picture-gets-more-curious.html has just convinced me that the answer to this question is "yes": given the large recent increase in vacancies in the past two quarters, the U.S. unemployment rate ought to have started to fall. It did not.
That means that the chances are now very high that our cyclical unemployment is starting to turn into structural unemployment, as businesses that seek to hire and have the cash flow to hire still find that the currently-unemployed applying for jobs don't fit inside their comfort zones.
The solution? The last time the U.S. was in such a situation was at the end of the 1930s. Mobilization for total war cured the incipient structural unemployment problem with ease. The solution is to rapidly boost aggregate demand: quantitative easing, raising the Federal Reserve's inflation target, banking policy to take more risky assets onto the government's balance sheet, and fiscal expansion. Time is of the essence. For the odds are now better than 50-50 that two years from now we won't have the ability to quickly and cheaply reduce unemployment to normal levels through boosting aggregate demand.