Have you thought about having a task start date as well as a due date? You would also have current tasks view (startdate < current date < due date. That way you could add tasks for the future but they won't clutter up the tasks you are currently working on.

If you did that you could organize tasks into future, current, and overdue. I tend to have things I need to do in the future, but not necessarily right now. However, I still need to remember them.

Maybe this would clutter up things too much but it's a suggestion.