Most economists do agree that a minimum wage at a high enough level is destructive and would increase unemployment. What they disagree about is the answer to empirical questions such as “what is the magnitude of the unemployment generated by raising the minimum wage incrementally from $7.25 to $10.10 over the next two years” and policy trade-offs such as “would the gains in higher wages for some offset the losses in wages for others,”
This business week story is indicative of these issues:
So, I don’t think you’re missing anything. I think the economics profession, having sowed the wind of model building, is reaping the whirlwind of politicalization.