What about them? I'm sure they would appreciate being fairly compensated for the labor they provide. Minimum wage is one means of protection for employees from abuse of power by businesses. As I said before, living wage to me means more than just enough money to barely get by. It's true that living expenses vary across the country. This is why there is a federal minimum wage, but individual states (not sure about counties/cities) can make their own minimum wage above the federal minimum. This gives a general level of broad protection across the country and allows for other places to raise it as necessary if living expenses in that area are higher than average.
There are other, and perhaps better ways to accomplish this but everything has its drawbacks. Ziggurat mentioned expanding the earned income credit, but there are two reasons I don't like that idea much. First, it doesn't help someone who needs money soon. That minimum wage gives the person money they can use now to pay rent, gas and food. The earned income credit only helps at the end of the year, unless it has other uses beyond what I am familiar with. Second, it gives companies incentive to pay their employees poorly. With a minimum wage the money going to the employee comes from the business. Granted, this can be passed in part onto the consumer, but only to an extent as there is a price limit at which people won't purchase a product anymore. However, with earned income credit, it comes from the government, which in turn comes from taxes. I don't like the idea that the burden of paying employees a decent wage gets taken away from the business and onto tax payers in general.
Companies and the higher ups within them don't have the greatest track record for treating their lower rung employees with care. I just want businesses to share the revenue and profits earned from the business more evenly among employees. A minimum wage is one way of doing that, and like everything it has its drawbacks.