I'll start by saying I think I agree with a $15 minimum wage (and I'm lifelong conservative attempting to start a small business in retail)but I do see how it could really harm a small, medium or large operation trying to scrape by.
Maybe we should consider cutting  income tax on the lower end. This would help people with entry level positions, and help business owners that are having difficulty getting by.  Then offset the cuts to lower earners by increasing  taxes on higher earners.  Lets be serious, someone earning $200,000 a year isn't going to notice another $5000...I know they are taxed heavily as it is, but I think they will be okay.  Plus this should help pull some dollars from the business owners who effectively abuse the system by paying only minimum wage and take millions in profits for themselves...it happens, I know a few. These are the same type that apply for government grants and then do nothing with them but split up the cash with their partners to buy a third cottage.