My take on increases in minimum wage, especially large increases, is that these increases eventually raise all hourly wage earners. A person making $9/hour as an assistant to the assistant french fry manager will want more per hour than the new, rookie assistant to the assistant french fry manager. $15/ will be the new base hourly pay. The $9/ worker who has been there 1 year will want more than the $15/hour rate so there will still be a wage disparity.
A drastic increase in the minimum wage, will not necessarily lead to lost jobs, it will contribute to higher prices. Higher prices will reduce the buying power of minimum wage workers. There will always be working poor. Someone has to do the low skill jobs (van expediting), unless Bernie gets elected and levels the playing field. Keeping the minimum wage in line with the cost of living is fine. A drastic increase in the minimum wage will do nothing, in the long run, to help the people it is intended to help.