This reads more like the"engineering manager" has had a sales role for too long. I think most frequently this is at the VP level.

The direct eng manager (or PM sometimes) should be in a position to fight against this sort of absurdity, give the IC a few days to scope the project, etc. One of the eng managers at a previous employer wasnt a great technical mind but was stellar at playing defense against managament. We all had great respect for him repeatedly taking it on the chin for his team.