Let them have their $15/hr. You know what's gonna happen? People in currently higher paying jobs will, then, demand raises. You don't go to technical school, get a bachelor's, have years of experience, etc. to only get paid a few dollars more an hour than (not saying these are the only people with these jobs, but the credentials to get it are at this level) a 16 year old who takes your money at the register.
If the demand isn't met, people will leave their jobs and flood the food/service industry, leaving the higher skilled jobs open. Then those employers will incentivize people to come back by increasing the wage....because they need workers in order to operate. $15/hr will be the new $7.50/hr, one way or another
At the end of the day, the low skilled, minimum wage workers will still be at the bottom of the rung and their purchasing power will be the same as what it is now, because when they make $15/hr, somebody already making $15/hr will get $30/hr when everything is adjusted. Prices will go up in the wake of all this new spending, as suppliers are going to want to maximize profits. Once the market corrects itself to the new standard, the "$15/hr or we're walking out" people are gonna be in the same situation they're in now.
Higher wages should not be a reward remedial work. Higher wages should a reward for bettering yourself, developing skills, and becoming attractive to employers of tougher jobs than not everyone and their mother can do. There's a reason doctors get paid 100K+, engineers get paid 80K+, etc. It's because not everybody can walk in the door and do heart surgery or diagnose medical problems. Anybody can say "would you like fries with that?"
