These come around to me all the time, and within reason, I will always take a moment to prioritise and plan my work. Is it doable, what's the best way to approach it and who else's input do I need. I can then see how long it will take me, and what I can do to meet all the deadlines I need. No need to get stressed, as we're all human and can only do so much, but it's about keeping your head screwed on and thinking logically at all times.