[whpalmer4]

No, I don't believe it is possible to build a perspective that does what you want. You can only get the grouping you want in Project mode, but there is no way to filter out the non-due stuff there. You could find them in Context mode, select them and double-click to open a Project mode window that showed the containing projects, but you would get the entire containing project, not just the overdue action group. Rob's script with his suggested query works pretty well for this, except it grabs overdue projects and projects that would be overdue if not on hold or dropped, so you have to do some picking and choosing of the results. Rob, any suggestions for a better search?

If you don't assign a context to your action groups or projects, you can just look for them in the No Contexts bin with the Due filter, then double-click to get the focused window. Credit for the germ of this idea goes to Curt Clifton in a discussion about how to keep track of projects and action groups with no available actions.