How many times does a super-urgent task land on your pile? Try this response (rather than going into meltdown).
Dear task setter,
Thank you for your email. I’m sure that this has been on your plate for some time, but it’s now become an emergency in your world. I’ve got other things that I am managing in my world, too!
Please respond back with what your real deadline for this is, and what is the last critical moment that you can receive this from me so that you can move forward.
A response like this gets great results – if nothing else, you are likely to find out the real deadline and get the task setter to think about how they delegate tasks.
Try it and let me know how you get on.