A) There are fast food places that have fewer workers (maybe just the owner and family). They wouldn't have to worry about doubling wages. They could afford to keep prices low, thus screwing large chains out of business.
B) By doubling the cost of labor, you're making capital far more attractive. Fast food companies will rapidly attempt to replace most of their workers with machines. Some workers are obviously necessary, but one can significantly cut down if one is willing to buy expensive machinery.
C) The least skilled workers (usually member of ethnic minorities) will be priced out of the market. They will be the first ones fired due to B, and they're not going to be hired by anyone at $15 an hour.
D) By paying fast food workers $15 an hour, you're going to encourage people to pursue fast food jobs instead of getting a college education. Why go to college for 4 years just to get an entry-level position that pays no better than McDonald's? In fact, this is what happened in Spain with the construction industry.
E) Products are bought at the margin, not in the abstract "how much do I think food is worth". At the margin, there will be people who are priced out of the fast food market if prices increase too sharply. This is especially true for poor people, who literally can't afford to spend more on fast food.

So as usual, lefties like you ignore all the inevitable side-effects of a do-gooder policy, side-effects that happen to be far worse than the supposed benefit.

As for some facts:

"We found mean price elasticity estimates ranging from 0.27 to 0.81 (absolute values), with the highest price elasticities for food away from home, soft drinks, juice, meats, and fruit and the most inelastic demand for eggs. "

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2804646/