Liberals (and children) make the mistake of thinking that the Minimum Wage is some sort of a guarantee of higher wages. It isn't. It's a RESTRICTION on whether an employer can hire at all.
The flaw in their thinking is two-fold. It's due to the combination of a high sense of self-worth and an incorrect understanding of the value of the job. If the job isn't worth a mandatory $15/hour, then it won't be offered. Period. And if an applicant's assessment of his own worth is significantly higher than what a would-be employer thinks, again, there will be no job.
The bottom line is that when the law dictates that employers must pay their employees more than either the job or the employee is worth, low-end employers have little choice except to not hire.
There will always be employees who DO earn that much. But, unless they're related to the owners, it's going to be because they're worth that much. They bring in that much value to the business. Such people would have been earning more than the minimum wage anyway, either due to promotions or by finding a new job where their skillset is properly compensated.
That's why the minimum wage is such a bad idea. All that it really does is to eliminate low-end jobs.