My feeling is, if the team loses 10 or more, the GM has to go.
If the team loses 10-11, for Joe Judge's fate, I think it depends on more factors, but he's on thin ice. If many of the losses come down to coaching/mistakes as the main factor, then I think he has to go. If the team loses 12 or more (i.e. they go 2-6 from here), he's gone.
In other words, Judge has slightly more rope than DG.