Two people need work by the end of the afternoon. Saying yes to both may postpone the awkward conversation, but it does not create more time. A clear priority discussion makes the constraint visible while there is still room to choose.
Put both requests on the same page
List the requested outcome, deadline and your best estimate of the work remaining. Mark uncertainty rather than presenting a guess as a precise commitment. Note any dependency that could delay either task.
Then identify who can resolve the conflict. If different managers are involved, follow your team’s process rather than silently deciding whose request matters more.
Offer a concrete choice
A hypothetical message might say: “I can finish the summary today or complete the slide revision today. Doing both requires moving one deadline or reducing its scope. Which outcome should take priority?”
Use neutral language. The problem is a capacity constraint, not evidence that one colleague’s work is unimportant. If a smaller deliverable would help, describe exactly what it would contain.
Confirm what changes
Once a priority is agreed, update affected people and record the new expectation. Do not assume everyone saw the conversation in which the decision was made.
For the original task definition, see clarifying work before starting. Better priorities depend on knowing what each request actually requires, not simply ranking the urgency of the messages that arrived.