The latest GDP revisions have tightened the relationship between employment and GDP in this cycle compared to the unrevised data. Some advocates of an AD-AS story are ready to say, "Nothing structural to see here. The aggregate production function is alive and well. Move along." But check out these charts, from Calculated Risk.
I am mentally trying to overlay the GDP chart and the employment chart. Until the two most recent recessions, the bottoms of the icicles look similar. That is, if GDP bottoms out at 97 percent of peak, then employment bottoms out at about 97 percent of GDP. But the two most recent recessions are different.
I think that one can still make a good case that a lot of current unemployment is structural. I have nothing against trying an all-out monetary expansion to try to see what it can do, because I think that the long-run inflation danger is fiscal, not monetary. But I think that ongoing factor-price equalization is the main labor market story of this century.