I don't know about you guys, but in the real adult world of employment- regardless of profession- one does not hold anothers job over their head as motivation. Nor does the notion of the carrot on a stick (playoffs=job retention). If I worked for a boss who thought that was an effective form of motivation and basically told me they were beginning to look for my replacement, I'd assume my tenure was coming to an end. And even if I achieved whatever measure of success he hinted at to ensure my future, I'm not sure I'd want to continue working under those conditions.
I, for one, do not believe reaching the playoffs are necessarily a component of coaching. I think Rivera should be gone regardless, and had it not been for the time it took to bring in Gettelman, Rivera might have been replaced before this season. The GM knows who he wants to coach this team, and Gettelman is no different, except he wasn't given that opportunity this season because the FO took their time in hiring him.