Whenever I felt overwhelmed by my workload, I found myself fighting the urge to just give up and sleep. The result was a great deal of assignments in college that I had left only partly done. At the same time though, I found my most productive moments to be at the times just before a deadline. I would finish work in a fraction of the time it normally took me.
I think the difference between the two situations is the feeling of hopelessness. When there really is no way to finish everything, it's hard to do anything other than just give up.