I take it as a challenge and a learning experience. First step is to prioritize the things at hand so that I tackle the most important thing first and go accordingly. Never let the stress overcome your own performance. If dealing with different departments who may not be aware of what's on your plate, let them know of a logical time-frame for a response with a reasoning why it would take that long. People are appreciative if you tell them the above two reasons rather than brushing it aside as unimportant.