It is the above mindset that needs to be changed. Minimum wage jobs are not supposed to pay enough for a person to fully support themselves. They are jobs for the unskilled. The majority of whom are under 25.
The rise in minimum wage in the past hasn't changed the fact that they can't live off of it alone. If you pay the unskilled at a level they can support themselves, then:
1) What is the motivation to obtain a skill set?
2) What do you pay those that develop a skill set?
3) If the unskilled get a raise, what do you suppose the skilled workers will want?
4) If the raises start working up the skill set chain... what happens to the overall costs of goods?
You see, it is a circular problem. That is why the mindset needs to change. No increase in the minimum wage will ever be enough for a person to fully support themselves.