not a teacher
I think the expression "blue in the face" is most commonly used in reference to talking.
The vast majority of the 103 examples in COCA are of this sort.
We can argue until we're blue in the face, but when you're outvoted, you have to accept it.
I could explain it until I was blue in the face, but there's only one way to describe it.
They've got a right to cross-examine them until they're blue in the face!
I know I can make all the suggestions I want until I'm blue in the face, but it's their team.
This end-of-the-world story they could recount until they were blue in the face.
I have never yet seen a whole roomful of people lie themselves blue in the face.