Lawyers are renowned for not doing something until ten minutes before it is due. I admit, for some people, the only way to write is under pressure. If you find that produces good results, then by all means, stick with what works. But if you constantly find yourself thinking “I wish I would have had more time to work on that,” then consider making a change.
Make an earlier deadline
Not in your head, on your calendar. If your response brief is due on March 4, then mark it on your calendar as March 1, or March 2.
You might not get the same adrenaline rush, but you might find yourself doing better work. Finish it a day or two before, then spend an hour polishing it up on the actual due date.
Make an outline
If you refuse the previous idea, how about an outline? Creating an outline a few days before will let the ideas start to simmer in your brain. If you are completely unprepared for one part of your brief, now you at least have the option of doing some extra research.
Creating an outline will also make your brief more organized, more readable, and more persuasive.
Schedule something else on the due date
Instead of blocking off your afternoon on the due date, schedule a client meeting. If you are literally unable to write the day of, you will force yourself to work on it earlier. This could land you in dangerous territory if you still procrastinate, but it also might force you to make some much-needed changes in your work habits.