A minimum wage hike of $15 per hour is possible if one simple counter measure is taken. Instead of keeping the overtime rules at 40 hours per week, lower it to half, 20 hours per week. This simple supply shift will naturally raise wages so in essence, minimum wage can be raised without effecting jobs.
Companies will only pay workers 4 hours a day or 3 days a week so their costs won't go up per employee. The average worker will then have less hours but since most people on minimum wage have multiple jobs, it will make it far easier for them to keep those multiple jobs and spend more quality time at home while getting them completely off welfare.
One last point, quality of work goes up. Most minimum wage jobs are service jobs; service quality goes up because less drain after 4 hours.