I offer this, it may or may not be relevant. When one of my bosses came to me with a top priority that would mean disrupting my already filled schedule and I was already working on 3-4 other top priorities for them, I would make a simple statement, "X, you have already asked me to do A, B, C & D, as top priorities to complete on top of my own regular work. Now your asking me to do E and F. Which project, A, B, C or D do you want me to dismiss so I can fit either E or F because I can't do them all?"

It puts the ball back into the managers court, forcing them to manage. Plus they get to decide which task you can stop doing, thus your not at fault for not finishing it on their timeline.