I love your app.
I can filter on tasks without a due date but, what about filtering on all tasks that DO have a due date?
No, unfortunately you are not able to search for tasks with a due date. This is because you can search in a much more refined way. You can search by, date, priority, name, and many other filters. The today view will show you all tasks you have, as well as the 7 days (or any search up to 30 days).
Though, feel free to add this to our Votebox: http://todoist.com/Vote/