The effect of the minimum wage in American Samoa and the Northern Mariana Islands offers a good example of how there are two possible outcomes with minimum wages:
1) It is low enough to have such a small effect on the total labor force that measurement of outcomes is difficult.
2) It is high enough to have a measurable effect. The workers on these islands now have experienced that effect, unfortunately.
(I think non-subscribers can see the article if you google "minimum-wage realities".)