The only 'real' use of minimum wage is to help make sure things like slavery are not big issues.
TL;DR at the bottom of this post.
Most everything else with minimum wage is pointless.
in '12 about 73.5 million workers with about 3.5 million at or below minimum wage. That is about 5% of ALL workers.
Of those 3.5 million about 1.7 million where under 25, about 990 thousand with out HS diploma/GED. These people are probably in high school or college supplementing their coursework either to pay their way through school or to party ;-) Or even just for work experience. Wopper flopping your way through school looks better on a resume than playing world of warcraft 30 hours a week, even if you spent the money on hookers and blow (as long as you didn't get caught lol)
There are always going to be those who make less. Everyone has a chance to live the dream but sometimes that dream is a nightmare. How you live in a free market democratic system is up to you. You don't like your situation there are ways out of it... and often it is not as hard as it seems.
Point is the amount of people making the federal minimum is not all that high and in many areas is enough to live on if you are single. If you got kids chances are you got enough assistance to make it work fairly easily financially though it might still be a headache. It is just another one of those "War on somethings" like healthcare, LGBT, different Sexes, climate etc that really do not effect a lot of people until there is a law to change it and then it screws everyone over. I think the whole raising the min wage is to put people into higher tax brackets for a temporary boost in revenue.
IMO: Federal minimum wage should be abolished and replaced with State and local minimum wages. (almost done now) New York state just raised minimum wage this past January to $8 an hour and will be raised again next January. In New York City or Buffalo it is very rough to live on.. but in rural areas that is more than enough. I think one county out west somewhere raised their minimum wage to $15 an hour. I bet the cost of living is really high there.
Another thing to consider. If minimum wage is $8 per hour, I make $9 per hour at a semi-skilled job and then minimum wage gets raised to $11 an hour I get a $2 raise with my skill set.. unskilled positions get a $3 raise. Basically I got a pay cut.
TL:DR: not really much of a problem, just a scare tactic against the GOP and the 1%, IMO put minimum wage on states and local governments as the COL is different for different areas. and don't eff my pay up by raising it to what I make ;-)