Some people believe it causes people to lose jobs and others state that with a higher wage people spend more money to stimulate the economy.
There was no minimum wage when we had the Great Depression! I can't think of any recessions we've ever had that can be attributed to what the people (at the bottom) were earning hourly.
It's doubtful to me that if we paid people $5 per day as they do in some parts of the world that we would have a more robust economy.
Yes if the minimum wage is higher there would be more competition as employers are likely to invest more time in hiring the "right employees" and in the proportion to what they need. However I have never bought into the thinking "I can't get a job because they're paying you $10 per hour or whatever".
Having said that I believe a lot of folks want to turn "stepping stone jobs" into careers these days. When I was growing up there were just certain jobs people worked to earn "extra money" or jobs teens and college students worked while going to school to pursue their "dream job". These jobs tended to require little skill such as fast food restaurants, grocery store bagger, stocking shelves, cutting lawns, retail sales associate, newspaper delivery and various other jobs.
Today most of these jobs are held by adults in their mid 20s and beyond! I can't tell you the last time I actually saw a real "paperboy"! That job is now held by grown folks driving around in a van. (No bicycles or pulling a wagon).
I believe the push is on to increase minimum wages to double digits because we have outsourced so many (manufacturing jobs) to other countries as well as signing some bad trade agreements. Most of the people waiting on you in fast food restaurants are "grown" men and women these days. Lets face it those high paying manufacturing jobs are never coming back to the U.S.A. Even many of the higher educated technical jobs are being outsourced to places like India or corporations are paying to bringing them to the U.S.
A combination of corporate tax incentives to hire Americans and raising the minimum wage are small steps in the right direction but neither will solve the lack of manufacturing and higher paying blue collar job opportunities. Paying someone $15/hr to flip burgers isn't the answer. I'm in favor of a phased in step increase up to $10.