Scenario/Background: I have two bosses, with one of whom I manage variable daily processes (priority 1), while the other one gives me longer term projects (priority 2). Due to the extreme variability of the daily processes workload, I am normally free to work on the projects whenever I am not busy with the daily processes - in fact, I have no deadlines on the longer term projects as long as I complete them within reasonable time.
If at any time the project boss asks me by when I can finish something, I normally state an estimated time with an ample buffer and often finish before that.
Recently, however, there have been entire weeks during which I was nearly 100% busy with the daily processes and thus had no time for the projects. My project boss noticed this and started setting deadlines - however, this meant that I often need to work after normal hours.
The problems started when the project boss started becoming impatient due to his own superiors' deadlines. On one day he came and asked me to finish something on the very same day, because the CEO needed it ASAP.
I had other personal appointments scheduled on that day (it doesn't really matter what type of appointments, or does it? It could be anything, doctor, kids, an old friend, a trip!) but canceled them out of fear of being fired if I didn't finish by the new deadline.
However, I now think that it's time to stand up for my... time, and thus I would like to ask what is the best, most diplomatic course of action to refuse sudden, last-minute deadlines - especially if they are in conflict with other commitments I have already made!