This is mostly for Serena based on her recent entry, but also helpful in general.

I got this in a training class.

If you have alot of people making ASAP demands of you, what you need to do is write down all of the tasks you need to do on your whiteboard in priority order. Then, if somebody wants you to insert something ASAP in the list you can show them all the stuff they are pushing back which may help them see exactly where in the list their thing needs to be. (Or even if it's as important as they think.)
The other thing is if you have a supervisor you don't have to say no, you can just ask them to clear it with your supervisor to insert their task in the list. That's why they make more than you.

Anyway just a helpful tip I picked up in class.