I don't object to the idea of an increased minimum wage, but I don't understand the need to tie minimum wage to living wage either. There are plenty of people in our society who don't need their wage to be "living". Dual income families, and teens come to mind specifically.
There are also dangers in making the minimum wage too high. The more it costs, the less economical it becomes to have employees at the minimum wage level. To an extent business will absorb these costs and pass them onto consumers, but beyond that extent it becomes better off not to have the employee at all, at which point everyone suffers.
I would just urge caution, because tying the minimum wage to a living wage will make it much higher than it needs to be for a well functioning society, and it will hurt the people its trying to help.