You claim raising the minimum wage would never raise prices nor cause unemployment to rise. Ok, let's set it to $1000 a hr. Do you really think that would have no effect on either of those? Maybe there's some range on increase where the effects are offset by other effects but it's not lying to believe those effects will become real at some point.
Realistically speaking, though, most arguments are over minimum wage hikes that only affect profits and won't even have a minimal effect on prices. $10 -> $12 isn't even going to cause prices to rise, let alone have an effect on employment. It'll go straight from profits to paychecks.
I can think of only one instance where raising the minimum wage actually affected employment, actually, and that was because it was set at first world levels in a third world environment.
I think you're wrong in thinking that businesses will just give up, and take lower profits. No. They're going to cut hours, fire anyone they can, etc. to maintain their existing profit levels.
But no, they don't just sit there and take it. They pile money into think tanks and advertising campaigns in order to try to sway public opinion (see above).
One of my favorite tactics is when they pretend that robots that do minimum wage jobs all cost $minimum wage + $1 and raising wages is simply going to make them all go out and buy those magical robots.
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:
It's the economists who poorly design studies with the intent of demonstrating that it either causes prices to rise uncontrollably (which it doesn't), causes unemployment to rise (which it also doesn't) and who pointedly never, ever, ever look at the effect it has on profits (it is savage towards profits, which is why the marketing budgets for stuff like this gets approved: http://kron4.com/2014/07/18/new-sf-billboard-says-workers-wi...).
They all know where the money is in their profession: it's at ideological corporate think tanks. If you can tread the fine line between not lying and saying things which they really like you've got a good career ahead of you.
As it happens, 'moral' arguments that say that you shouldn't raise the minimum wage work better when you can claim that it will hurt the people it is designed to help. Those arguments fall flat on their face when it becomes apparent that raising the minimum wage just transfers profits into workers' pockets directly.