So far, the evidence doesn't seem to support that theory. Rather than finding jobs, the long-term unemployed continue to be out of luck.
We now have three months' worth of job market data since the benefits program expired. The chart below shows job-finding rates for the long-term and short-term unemployed. Notice three things: First, the short-term unemployed have a much better chance of finding a job than the long-term unemployed and always have. Second, the short-term unemployed are seeing a steady improvement in their prospects, but the long-term jobless are not. And third, there's been no major shift since the benefits program expired at the end of last year. (The chart shows the data as a 12-month rolling average, which could obscure a sudden shift. The un-smoothed data, however, doesn't show a jump either.)