[mrweasel]

Letting people know that their request will interfere with projects for others, and they need to clear it with those people, not you, is always a good idea. People tend to view their projects as more important and will always put their needs before other, especially if they are pressured by their own deadlines. You don't want to be the person that pick which project gets done first. You'll always pick the wrong one.

One weird situation I often encounter is people wanting something on a deadline, but there isn't actually enough time or circumstances have changed. It's highly unproductive when people just keep repeating that a deadline must be meet, regardless of circumstances. What I have resorted to in these cases are not saying no, but asking what they'd have me do. That often removes the expectation of magic or whatever management believes is going to intervene if you just keeps pushing.