I think the trouble with the minimum wage debate is that a lot of people just look at the lowest jobs on the totem pole: the fast food employee, the convenience store cashier, or any other job that a high schooler would be qualified to do. The real problem comes with jobs that are a step up, maybe in skill, difficulty, and/or responsibility.
One specific sector I have in mind is the EMTs and first responders. Rescue squads around the country are having difficulty finding volunteers, and one of the only ways of offsetting this shortage is by hiring people to pick up the slack. Our rescue squad starts people out at $12.50 an hour, and this is a job that requires being up to date with certifications and training. It is also one that involves a lot of responsibility, as you are responsible for the maintenance of people's lives during transport. If minimum wage were to raise to $15 an hour, not only would we have to give everyone who works for the squad a pay increase on our skeleton budget, but they would then be making the same wages as those other low skill, low responsibility jobs. Not only would this hurt the rescue squad in having to pay their employees more, but it would influence their employees to seek easier jobs.
Another area that would be affected is in the landscaping business. Sure, lots of these jobs are filled with illegals, and if they remain they will probably still be satisfied with their current wages. The going rate for part time labor work around here is $15 an hour. It is a higher paying job than a cashier or fast food worker because there is labor involved. The increase in the minimum wage would put pressure here as well, since the legal workers would now have to be paid more to justify the job difficulty gap.
Solid entry-level jobs out of college start in the $15-20 range, and oftentimes stay there if there is minimal movement up the ladder. The same goes for hired hands of labor jobs. The incentive to aspire to these jobs would also be decreased.
It is clear by now that im not an economist, but im just looking at the current state of the job market in terms of pay, and I think it is logical to believe that an immediate doubling of the minimum wage would put a lot of negative pressure on many fields of work. Im am actually in favor of increasing minimum wage, but not in such a sudden and drastic way.