$15/hr would be a 107% raise over the current fed min wage. I assume everyone making more than min wage in the country will also demand to get a 107% increase? Because what if you're currently making $16, $17, $20/hr...?? Right now, I'm a 2nd year driver and make $18.45/hr. It took me working my butt off until the age of 35 to make this. Do you realize how pissed me and others would be if a 16 year old at their first job at McD's immediately started at $15? There's millions of college grads that make less than $20/hr. Many of them aren't any more than $15. How would they feel?
There's a million problems that would arise from such a drastic increase but no one wants to think about the consequences.
The minimum wage is not meant to be a family supporting wage. Why is this even debated as such? It's a wage to start people off early in the workforce. Mostly kids. If you are 30 years old making minimum wage, you need to reexamine your life.
A fear wage is what people are willing to be compensated for the labor they do. They don't like min wage, no one is putting a gun to your head. Work harder in life and go further. There should be no federal mandated minimum wage. All it does is set a minimum that employees get to use. If there was no set minimum, you'd likely see higher wages as employers would be competing for better help.
My last point will be that such a drastic increase would would quickly speed up inflation. Everything would have to go up, and it would go up faster than we've seen perhaps ever. Ultimately, that new shiny wage won't be worth much more than today's min wage.