Single payer health care and "competitiveness"

Greg Mankiw has written the post I've been meaning to write on the odd view that one often hears in the media and from politicians that moving to a single-payer health care system, like that in Canada, would make US firms that provide health insurance more "competitive". This view implicitly assumes that workers care about pre-tax compensation rather than post-tax compensation, which seems unlikely.

Greg's care in distinguishing between the short-run and the long-run is well-taken, particularly given that many of the firms pushing this idea are unionized legacy firms like the "Big Three" automakers. I can understand why the long run might not be really salient at GM and Chrysler just now.

The real puzzle to me, though, is why unions (such as the UAW) also advance this idea. Unlike the firms, which gain in the short run if it takes wages time to re-equilibrate, the unions stand to lose in the short run as the quality of their health care would decline immediately upon the government taking over the payments, and their taxes would increase as well. Wage increases to compensate and return their net compensation to market-clearing levels would come only slowly thereafter.