1/ Most folks who are on the minimum wage are not actually supporting a family on the minimum wage. A tiny fraction (think less than 4%) of workers in the US earn the minimum wage, the rest earn more.
2/ The minimum wage is a training wage. It is an introductory wage to try a new employee out (since much current labor law limits how much you can research a new employee in advance). It is a second job wage. It is a wage in retirement as people slow down. It is a teenager wage.
3/ All those types of job openings go away when the minimum wage is raised substantially. BTW, it is estimated that 2/3 of minimum wage earners are not poor, but are middle class or richer (2nd jobs, kids jobs, etc).
heritage.org/jobs-and-labor…
heritage.org/jobs-and-labor…
4/ In fact, the main difference in earnings between the median and the lowest 20 percentile earners is not the wage rate but the hours worked. coyoteblog.com/coyote_blog/20…
5/ Increasing the avg wage rates of the poor (lowest 20th percentile) to middle class levels yields $6,335 a year while increasing the poor's amount of work done to middle class levels yields $28,844 a year. Clearly to help the poor you would focus on hours not wages.
6/ Poverty generally comes from not having enough work, not the rate at which it is performed. And increasing minimum wages can thus be detrimental, as it tends to reduce work available and particularly work available to the unskilled.
7/ And it can be devastating for that first job that starts unskilled, under-educated poor people on the road to building skills and job experience they can leverage into better jobs. 
8/ I wrote more about how well-intentioned labor regulation often hurts unskilled workers here:
cato.org/sites/cato.org…
cato.org/sites/cato.org…
