VoxEU has a shorter version of a longer working paper produced recently by Neumark, Johnson, and Mejia on projections of skill shortages (HT - Mark Thoma). I've been working through the working paper for my NBER chapter, particularly since it now looks like I'm giving a separate presentation on shortages. As you all might guess, I'm skeptical of this sort of forecasting. They don't have a good track record, in part because they can't project market responses. Often it's simply an extension of current supply and demand trends.
Neumark mentions a recent projection by Carnevale and his coauthors. I heard Carnevale present this at the Georgetown STEM workforce conference I went to a couple weeks back that I mentioned on here.