Unemployment and the Minimum Wage---what are the main counter-arguments to Card and Krueger? Card and Krueger's paper (AER 1994, "Minimum Wages and Employment: A Case Study of the Fast-Food Industry in New Jersey and Pennsylvania") uses a difference-in-difference identification strategy to identify the causal effect of a minimum wage increase on unemployment. (A summary can be found here.) The main finding was that the increase in the minimum wage had a negligible or even non-existent effect of employment. There have been several criticisms to the paper---including criticizing the quality of the data or the fact that employers might have anticipated the change.

My question is, what are the main economic explanations for why employment did not significantly fall? What other evidence could be used to test these explanations?
Isaac Sorkin, a grad student at Michigan, has addressed this. Here is Miles Kimball blogging it, Isaac Sorkin: Don't Be Too Reassured by Small Short-Run Effects of the Minimum Wage, Jonathan Meer and Jeremy West: Effects of the Minimum Wage on Employment Dynamics, and The Economist—Destination Unknown: Large Increases in the Minimum Wage Could Have Severe Long-Term Effects. The main argument there is that previous work measures short run elasticities, which are less responsive than in the long run. You can surely find more by checking Sorkin's citations.