Simon has a good point about regional economies that a national minimum wage could cause serious damage to the economy.
If a factory in small town Georgia is paying $12.00 per hour to its skilled workers producing widgets for the export market is forced to up the wages by 20% the market might not bear the price increase. The factory might have to close.
I was actually in a situation like this a few years back where our labour costs outpaced the development of technology to reduce the labour needs. The company folded as our international buyers purchased from other countries who could produce for less cost.