Buttons840 parent
The ultimate exists whether or not you communicate it. I would hope that with enough tact that truth could be communicated.
The main thing is that if someone isn't going to do something in normal circumstances, an ultimatum is really for yourself to be done with waiting.
Just be careful - some will see it as having their arm twisted. You may get what you want in the short run, but in the long run, when you negotiate with leverage, people dislike that.
It is the nuclear option, and you will lose the trust of your leadership chain.