In theory it sounds okay. Except in reality some people don't have a choice. They take whatever is offered. At this point, with all of the talk of illegals etc., nobody has pointed out that bottom wages have dropped down to near illegal levels.
I was recently offered maid services from someone outside the metropolitan area for something a little above four bucks an hour. The woman drives down to the city three days a week to clean toilets, walk dogs, wash dishes and clothing for something like $50 bucks a day cash. I believe she's working a 12 hour day, not including drive time.
And who decides when people don't have a choice? If someone offered her a job at 10 cents an hour would she take it? Of course not, ergo she has a choice. The problem with minimum wage is it assumes a certain amount of income is fair and another amount is not, across the board. Is digging a ditch in the hot sun for 5 dollars an hour the same as flipping hamburgers? Shouldn't the ditch digger get 6 dollars an hour? What if I offer you a job in my bicycle repair shop for 3 dollars an hour because it's all I can afford to pay you, but you want to take the job because you primary goal is to learn how to fix bicycles? According to the government, you are not allowed to work for me. My point is, when the government gets involved more people have fewer choices, no one is any better off, and more people end up unemployed.