This is why I think we need to move away from a mandatory-employment economy entirely - as automation improves, we may find ourselves at a point where "It's a bad job, but somebody's got to do it" isn't true anymore. Of course, in order to get there, we need to find a way to transition out of an economy where work-saving automation is demonized because it replaces jobs. But, once we find ourselves in a place where jobs aren't mandatory, I could actually agree with the libertarian position of abolishing the minimum wage.
At present, there's too much a power difference between employers and employees. Who among us has ever actually been able to negotiate terms of employment, and who's had them dictated by employers (whether literally, or "If you don't take these, somebody else will" implicitly)? A few readers probably have been able to make that choice, which is great for them, but I'm fairly sure most people (much less most people reading the thread) haven't. If the average person could legitimately get by without needing to work, then there'd actually be a possibility for negotiation. As it stands, employers just have to make employment better than starvation, which isn't exactly a high bar. Most markets aren't sufficiently competitive AND unsaturated with applicants to undermine this, and when you've only got one or two potential employers for a given skill set in a given area, it's a fair bet that nobody's going to raise wages to earn better employees, thereby creating a permanent cost for a transient benefit (once everybody else raises their wages to match).