Like most issues, there are good arguments on both sides of whether to raise the minimum wage. I worry about mom and pop businesses. But I'd like to see workers able to make enough money to live.
The federal government has authority under the commerce clause of the constitution and has set the minimum wage for a long time. If that were unconstitutional, we would have known that a long time ago.
Robots are coming regardless of the minimum wage, and as pointed out, maybe faster due to increases in the minimum wage. But robots will take more than just minimum wage jobs. In another 10 years you'll see automation of almost every profession, and in 40 years, robots will do most of the work. A much bigger problem than whether to raise the minimum wage. If you want to rebell about something, that's something that will probably be worth rebelling over.