I wouldn’t count on a great deal of positive spillover into the rest of the economy in most places. The minimum wage definitely needs to be raised but I’m not sure about a national rate of $15/hour. That’s probably sustainable in major metropolitan areas but not in poorer states.
Consider a grocery store in West Virginia or Alabama. It’s a business that already operates on razor thin profit margins so if you increase their cost labor costs by 50-100 percent, how will they respond? By a combination of firings and cost increases.
Consider Randy who works at the transmission shop across the street. He makes $18 an hour which he thinks is pretty good for his little town. Is his boss going to say, “Hey Randy, they just raised the minimum wage to $15 an hour, so now you’ll be making $25 an hour?” Absolutely not. He’ll still be paid $18 an hour until his boss can no longer retain people that will work for that little in that job.
It’s a hard problem and there really isn’t a simple solution to it.