So why do you want to encourage them to do less? Minimum wage teaches people that no matter how hard they work, they are going to get paid. The more we give them, to do the minimum, that more that lesson is driven home.
Right now, if I could pay entry level HS kids what their job is worth ($6-$7) an hour as opposed to $8.25 I would be able to pay my key people more ($12-$13). If HS kid comes in and works hard, doesn't just do the minimum, more money will come their way. As it stands now, and especially with a nonsensical number like $15 an hour, a kid learns that no matter what they do or how hard they work, they are going to get paid $15 an hour and there isn't anything anyone can do about it. They dont' like cleaning toilets, quit and move on down to the next one. Instead of seeing that if you do a good job, you will get paid more.
You also seem to think that welfare is going to go away if minimum wage increases. Which tells me you really have no idea how inflation works, and what an increase like this will do to prices, and that a certain segment of society wants to work but they simply don't believe the current minimum wage is enough, and as soon as it is higher they will magically have a desire to put in 40 hours a week instead of watching TV all day. Not going to happen.