This is [now possible][1] (thanks Trello!). From the sidebar of your board, click *Menu > Filter Cards* then choose one of the options:

> * Due in the next day
> * Due in the next week
> * Due in the next month
> * Overdue

This will only filter on the current board, but this seems to be exactly what you asked for.

  [1]: http://blog.trello.com/card-filter-updates-cards-page-sorting-checklist-copy-and-more/