Okay, so, I do a lot of IT stuff at work (not all my job but a big chunk).
I configure new machines, quite often. I get 24-48 hours notice, mostly, and then get 'I need this by x' or 'can you get it done for today I will need it'. It's stressful and annoying. It could be avoided with proper communication and some basic planning. As is true for most IT support... 
When I run into a snag (as in the case today), I sometimes have to get external IT support to help (I'm not trained or qualified and I don't know all the answers, plus I have a million other deadlines).
So, when I reply 'it will depend on another party, it's outside my control, I will do my best', the reply is 'I really need it today, can you please prioritise it'.
Other than applying head forcefully to brick wall, how do I deal with this?
(For avoidance of doubt, I have tried replying 'yes, it will be my priority but I cannot affect the timeline of the external party, and I can't guarantee how long it will take to find a fix'. This gets the same answer on loop).