My orders come through a somewhat matrix-style command structure. I report to one technical line manager, who decides and defines how things should be done from a technical point of view, but also need to work with a variety of senior managers to discuss new business requirements, projects and other commercial targets, i.e. what should be done. I also have my own staff to help me. My role is to be the middle man.
What I can do by a certain time will depend on how I can do it and how many of my resources can work on it. One of the senior managers I work with most often tries to get most of my (my team's) time by using coercion in the style of "This is absolutely higher priority than those other tasks. Someone will get fired if we don't finish that sooner!"
Maybe he doesn't always do it so explicitly, but uses subtle techniques like coming to talk to me in person in public and ask many difficult questions on planning and deadlines before I even started deciding those timelines. "Why can't we do this? How long will it take to plan this? This is very important, you know right?" etc. I am thus often forced to say "Yes, don't worry, we should be able to do it."
This has been going on for a while and I made the mistake of just following what he said because I had no other choice (and he's a senior manager after all), but now I realize that this has put me in the habit of taking on too much and overworking my team, often and regularly beyond capacity.
What can I do when someone higher in rank than my line manager comes and speaks like this before I even started planning or uses coercion/blackmailing when helping me set priorities?