As far as the net effect of minimum wage upon job growth and opportunity, opinions seem to differ widely both for and against. I don't find the job loss arguments convincing in the way that you do.
In general we are talking about a very small group of people. I can’t find figures for CT but nationwide the estimate for minimum wage workers is around 2%. Poorer states have greater numbers of folks working in these jobs As you point out, most are younger and less well educated. But significant number of minimum wage workers are heads of households dependent of their wages (often from two or more jobs) to support families, something conservatives constantly argue they want to strengthen.