I like to look at this issue from a slightly different perspective. Should we as a society mandate that people who are employed full time receive sufficient wages to live a certain lifestyle? Because all we are doing now is trying to bridge the gap with government assistance which is allowing us to subsidize McDonald's operating model. If people care enough to eat fast food, it should cost enough to cover the costs to produce the food, including paying an employee to where they could reasonably expect to live safely without additional assistance. If that raises prices to an unreasonable amount, fast food will have to adjust their model. I'm just not crazy about subsidizing an entire business model with taxpayer money just so fat people can enjoy a dollar menu.
Outside of the ridiculous bickering between bleeding hearts and conservatives, of which I fall decidedly on the conservative side. I've thought about this a lot lately. The short to medium run results of fast food workers getting their wage increase is that either fast food prices increase to account for the labor (which is actually difficult to do because lots of the franchises have "deals" that are set by corporate that they have to honor) or the market rejects the increases and lots of fast food restaurants close and the ones that don't close are able to stay alive with extreme low margin and extreme volume (Fast Food Wars, Demolition man, Taco Bell....). So in the short to mid range, either the increase is passed along to the consumer (demand will be effected to some degree) and a small amount of jobs (by jobs i mean fast food jobs) are lost (due to some degree of demand loss) or tons of jobs are lost and only the "best" fast food joints with the best employees (that are worth their salt, so to speak) will remain. In the long run, systems will be created to cut the fast food employee out (reduce the price of fast food, or at least the labor component), or at least increase his/her productivity so that a high wage will be sustainable, so at the end of the day, most of these jobs will vanish. There would likely, eventually only be one of two people per store, working and fixing robots or computers getting paid whatever their skill level is worth
The end result, is that people will either have to get better (justify their wage) or won't be able to work.
McDonalds (which I'll use as a stand in for all fast food and all low skill labor) isn't meant to support someone on their own. It does allow people with no skills an avenue to work (and at least get paid something, even if their income has to be subsidized). Increase the minimum wage and eventually either those people have to provide more value, or they just won't be able to work. That's the ultimate question. In one scenario, you could see that people (I'm not really talking individuals, but people on the lower end of the economic spectrum) either better themselves and get to where the lowest skill person can provide value to back up their wage (in a way that 100 years ago, a small percentage of people could read, so the lowest skill person was basically a rented mule, but now most people can read, write and communicate effectively thus can provide more value than a rented mule) or people will just stagnate and won't be able to work at all as efficiency marginalizes the employees whose value is less than their wages.
Of course, the two scenarios above aren't mutually exclusive, you'd likely see the later one happen then eventually the former one would (hopefully) come around....but to what extent would either of them occur and what problems might that cause....who knows.
Obviously for people to "get better" they have to be better educated and to better educate the lower end of the economic spectrum there will probably have to be better educational systems and some sort of culture shock in said economic spectrum. (the later probably being the hardest to achieve)
I'm not against a minimum wage, I think it's main factor isn't to "provide" a living wage to people, but it's to basically force innovation and rid a complex economy of low wage, low skill jobs. Of course, poorly timed and unreasonable increases in the minimum wage can be hurtful to the economy as a whole and the very people it's trying to help because it may be too much at one time and the people on minimum wage can't adjust their skill set (quickly enough) to justify their wage nor can the businesses that rely on low skill (a relative term) labor innovate quickly enough to keep themselves afloat