With these sorts of situations, I find that it's important to break the tasks down into small enough chunks that I don't have to worry so much about the hard deadline (I still put the hard deadline on my calendar) and focus on how to do the task. Things with hard deadlines usually are projects and involve smaller tasks before you can be ready for the deadline.

My example:

Writing a report involves many steps only some of which involve hard deadlines:
Give the draft to Alice for a review
Submit the final report to Bob

Other tasks fall along the lines of:
collect research
do calcualations
write a rough draft

For these unscripted tasks I just decide when I want to start on them and add them to my NAs or put a note into my tickle file.

My goal is to have my tasks completed before the deadline. Since most of my work involves corralling other people to assist, the tasks near the end term are pretty fluid and involve things like "call Carl about his input."

A