but that seems to ignore the spirit of the idea, that we should all be working except those supporting those who are.

Well, in this particular case I think you've nailed down the concept. Each working person has the opportunity to designate someone who takes on a supporting role, and I'd think this person would have to live at the same address to count. Sure this means that you could designate your brother who moved in and isn't working, but then that's actually closer to the real idea anyway right? To identify those who play a supporting role, regardless of how they're related? Who cares if it's my wife or my brother who assumes that role as long as we all can agree I get to designate one person.