"What incentive would they have to train for better paying positions"

Interesting that you say this. Last night I sat and had dinner and a conversation with one of our clients. She is the Executive Director of a college. In their recruiting lobby they have a life size sign that says "get the training and get a job paying $12 - $20 in 6 months"

I brought that to her attention, and she commented, if minimum wage goes to $22 an hour, there will be no incentive any more to go to college and get any degree or higher education, unless you are going for a $100,000 a year job.  She said if minimum wage went to $22 an hour, she can see that a major portion of the training they offer would likely never have any enrollment any more, it would potentially force them to close the college.