Amp has found pretty solid evidence that this is simply false. I want to hang on to this reference so I can cite it when the issue inevitably bubbles up again.
By comparing changes in employment in the two states (a procedure they referred to as “differences-indifferences”), Card and Krueger were able to estimate the employment effects of the New Jersey increase. Using this approach, they found that the differences in employment growth between the two states were not statistically significant. They concluded, therefore, that the minimum-wage increase did not lower employment in New Jersey.
The link has more general interest to us bloggy folks because Amp narrates a failed conservative effort to refute the study.