The best way to track next actions is on the Calendar. By Day/Date or Appointment. I also use my Tickler Folders by Month or Date.
I do have repeating Tasks [Next Actions] that are more of a Checklist which I use Outlook Tasks for with a due date. (I manage a Food Service Operation - so I have, @ Calls - Milk Order every Tuesday/Thursday, @Work - Inventory last day of each month, @Work - Approve/Post Monthly Schedule-1st week each month for next month.)
If I understand your question, you're not asking how to track when you need to do something on a certain day, but you need to work on something at any time up to a certain day that it becomes due.
The easiest solution may be to put the due date before or after the item on your Projects or Next Actions list. If you put the due date before the item and you are using an electronic system, you could sort by item and have all your items with due dates sort to the top so you can get an idea of priority.
You may also want to put a reminder as day specific information on your calendar like "Project X Due Today" so when you are looking at your calendar, you'll get a reminder. Of course if it was really, really important you could put day specific information on your calendar everyday tracking the due date - "Project X Due in X Days."