[Breathless]

My answer would be to communicate. How is your supervisor to know that you have other obligations by the same deadline? So I would listen to what the supervisor is requesting, giving a moment of your time and attention, then present the problem of, I currently have something else, of a urgent nature on my plate that requires my urgent attention, also needing to be completed within the same time line. This is how long I anticipate 'this' task to take.. and put the ball in their court. Sometimes, just mentioning that you have another obligation, and would like to assist with this task.. giving the other person (supervisor) the option to make other decisions too.. is the best way to go about it. Promise is your word, and your customer is extremely important, for obvious reasons..