I still don't really know what the desired semi-reasonable outcome is for Theresa May or really any of the Brexiteers.
It's clear what May wants is to kick out all of the foreigners (as many as possible) and the rest doesn't much matter to her, but I still don't get what she/they want within the framework of sort of realistic possibilities.
The EU isn't going to "back down" because they just don't give a shit and why should they?