Getting as much clarity on the task and on the time frame as possible, Sometimes, delegators will name a short term deadline because they simply haven't thought about what's really needed. Polite questions can help nudge them to a reassessment.
Informing the delegator of what else you have on. Don't whine, just state the facts.
If it seems that the new assignment (and the seniority of its instigator) will present an impossible workload with everything else you have on, then say, "Will you talk to XYZ [other delegators] to clarify my new priorities with them?" Some things you have to push back up the line!
Asking if there are other people you can work with to get through the various assignments
