Generally speaking, I prefer letting the market take care of wages. If a company is willing to pay an amount, and a person is willing to work for that amount, why should the government stop that?
Granted, some people are maximally employed at the current minimum wage levels. But, others could seek out better employment if they are willing to shower and dress semi-professionally. (We have a local Catholic charity that helps people with that if they need help in that regard.) But, increasing minimum wage decreases opportunities by decreasing jobs and by putting financial strain on stores that have those types of jobs. It especially limits teens being able to get jobs.
This is not a big issue for me. Indeed, I'm not aware of a single place near me which employs people at minimum wage. The hiring signs out front always show wages higher than minimum wage. So, sounds like a non-issue to me.