Fiona, are you talking about the Overdue item on the main screen of the iPhone/iPod touch app?
If you want a perspective that shows you upcoming due items, I would suggest you set Due Soon to 7 days (or whatever value works for you, there's nothing magic about it), and in OmniFocus for Mac create a context mode perspective grouping by due date, sorting by due date, showing remaining actions, due soon. You'll see everything that is due in 7 days or less (or already due). Be sure to turn on the option on the settings page for the iPhone app to enable Perspectives.
I find it useful to set up a similar perspective grouping and sorting by start date, showing remaining actions of any status, with all of the groups except for yesterday, today, and tomorrow closed. I use that as my tickler, and try to knock off most of the tasks that appear there. For particularly important items that do need to be done by some specific date, I'll add a due date as well as a start date, but it is relaxing to knock things off as they become available, before they have a chance to join the list of things that must be done or else. If I can do everything on the due list, make some progress on the tickler list, and knock off a few items from the flagged list (items not necessarily starting today or due today, but needing near-term attention), I'll have kept any fires from breaking out and my backlog from growing too much, and that's a day I'll call at least a moderate success.