While there are some who won't be affected no matter how much you pay them, there are a fair number of people who will indeed "work harder" at an increased wage rate. It could be a combination of reduced stress*, knowing they have a good thing going, feeling appreciated, whatever.
This has been my experience, and through proper use of probationary periods, employers that voluntarily pay significantly over industry standard can build an excellent workforce that performs well beyond the cost:output ratio of the ones staying at or below standard.
*Wealth doesn't buy happiness, but research says that it at least pays off unhappiness. Or, more accurately, you tend to be unhappy when you're worried about where your next meal is coming from and/or how you're going to pay the bills.
More specifically, if you can afford better stuff and/or good maintenance for the stuff you have, you're not sitting at work worrying about whether your tires/dishwasher/backache can be put off another pay period or two without catastrophic results.
That's great, but as a theory it does absolutely nothing to support the idea of a minimum wage. If you're getting paid more, but can get paid just as much somewhere else, why would you "work harder"?
Which, again, only affects employers paying the minimum. Generally, those jobs are interchangeable; whether someone who is only worth minimum is at Taco Bell or Taco Bueno doesn't really have any impact on anyone or anything.
It also effects those closer to the proposed minimum.
If someone who was making five bucks an hour over minimum wage is suddenly making two bucks over minimum wage they will likewise want a raise. And it ain't going to be enough to make up the difference.
Also an accurate observation at many employers, though those who keep up percentagewise do tend to attract better people.
