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.
- Other projects will be pushed out of the way
- Your deadline is not feasible, I can do it by this date.
- The cost/time of me doing something would be high, due to my inexperience in doing that task.
- I personally think it is a bad idea and a waste of everyone's time, but it's your call.
Things may work differently for others, but turning a "no" to a "yes, on my terms" is what has worked well in any situation I've been in.