I've found this doesn't apply if you remove the deadline entirely. If given a task and a week to complete it, I will start the task on the night of the 6th day. However, if just given a task, I'll start the task immediately - or at the very least, as soon as I finish what I'm currently working on. Whether I complete it within the week depends on whether it's a week's worth of work, but I can be fairly sure that I'll end up putting in more work than if I had the original deadline, and I'll probably have something equivalent in quality to the deadline-work after about a day or two.
