Raising the minimum wage WILL increase unemployment. That's Economics 101. Companies are going to find ways to fire people, or give them fewer hours. Raising the minimum wage to something like $15 would be ludicrous.
Reality disagrees :) Germany introduced minimum wage recently and the opposite of your prediction happened.
The argument didn't match reality because it completely ignores the growth of purchasing power that is a consequence of higer wages.
Actually this is pretty much a model for what would happen to McDonalds in the US:
http://uk.businessinsider.com/mcdonalds-in-australia-vs-amer...
And if Econ 101 states it's true, then Econ 101 is wrong too.
Here's a more fact-based explanation, with links to studies and comments by economists: