The question is, was, and will continue to be: why is unemployment high? David Andolfatto (see here:http://andolfatto.blogspot.com/2010/12/is-deficient-demand-hypothesis.html) is asking if the deficient demand hypothesis is a reasonable explanation for high unemployment given some turnover statistics. It is a very interesting discussion. I want, though, to take this issue back to general principles and approach this logically.
Empirical fact 1: Unemployment is high. Note, as a supporting fact, that industrial capacity usage is still pretty low, but climbing: http://research.stlouisfed.org/fred2/series/TCU?cid=3 .
The deficient demand hypothesis suggests that firms are not employing people at as high a rate as before (demand for labor is low) because the firms themselves are facing low demand for their products (revenue is down). This has much intuitive appeal, I dare say. Sales are down, so why do I need to produce as much stuff? This squares with high unemployment and low capacity utilization.
But, which demand is deficient? Personal consumption (mostly households; this is the C in the GDP identity of GDP = C + I + G + (X-M)) has returned to its peak: http://research.stlouisfed.org/fred2/series/PCECC96?cid=110. Note that is in real terms. In nominal terms it's a little bit higher than its previous peak. Government (of course) consumption and investment expenditure is increasing: http://research.stlouisfed.org/fred2/series/GCEC1?cid=107 again, in real terms. The deficient demand appears to be in private investment: http://research.stlouisfed.org/fred2/series/GPDIC1?cid=112 .
In other words, households and government are spending as much or more than before the recession, and definitely more than during, but investment remains far below recent history. Go back to 2003 and that's about where investment is. So clearly there is where the deficient demand is. Now, of this private investment, the item that has fallen off the most is housing. This again should be surprising to no one.
So let's say you are a company that sells construction materials. Clearly the demand for your products has fallen off, so you don't need as much labor and capital as when demand for your products was higher. Thus certain types of demand are deficient, but demand generally cannot be said to be deficient. As I have illustrated, spending is high from C and G.
What does this have to do with anything? Well, there is a strong correlation between lack of demand for new housing and lack of demand for housing construction workers. No amount of structural problems is required to explain that issue - in other words stuff like sticky wages aren't necessary here. Too many houses - that's the problem.
So the relevant question becomes manifold. First - specifically which industries are experiencing low demand? Second - why are those industries experiencing low demand? Those discussions are few and far between from what I can see.