The concervative issue with the concept of increasing minimum wages centers around value, as determined by supply and demand. And they are correct. Most (all?) entry level "McJobs" aren't worth 10, or even 6 bucks an hour. They are too numerous, and require too few qualifications to fill, to retain any real value, beyond the fact that those positions MUST be filled in order for those companies offering them to function.
But this isn't about determining value, it's about what's best for society writ large. These jobs are becoming the new primary employers in this country. We are a service sector economy. And becoming more so every year. Either these jobs (which are becoming the largest employers in the US) start paying enough to support independent life, or we get a lot more dependents. To put it bluntly, we either choose to let our poor (who are going to grow in size as these McJobs employers increase) die, or we choose to support them, at least as far as basic life sustainability goes. So choose. Let our poor die, or support them. If you choose the former, then fine, end of discussion. If you choose the later, then you to accept that if these jobs don't pay enough to live on, a prospective employee has the option of NOT working, and still being able to live.
So, choose. Let our poor live on the tax payers dime, or let them die? Either we get rid of welfare, or we increase the pay of these jobs.