I predict the opposite is going to happen. Most proponents of BI also propose lowering the minimum wage. So let's suppose you're on BI receiving $12K a year. That's about enough to put a roof over your head, leaving very little for food or anything else. You see a clerk job advertised for $5 an hour. You don't have to take the job, but that $5/hr is the difference between eating rice and beans yet again or actually having a little bit of meat with your meal and being able to afford an occasional XBox game.

The big difference I see is that truly unpleasant and unsafe jobs will see wages rise. Being a clerk is not a great job, but it's not a bad job unless you have an awful boss. If your boss at the grocery store starts giving you trouble, it becomes much easier to just walk away and eat rice and beans for a while until you can find another job.