Let desperation belong to the person who actually needs the immediate answer.

In any negotiation or standoff, one party usually needs an answer more urgently, and that need shapes what they will accept. If it is not you, there is no reason to adopt their timeline as your own. Absorbing someone else’s urgency is a common and expensive habit.

Ask who actually needs this resolved today. If the answer is not you, respond at your own pace without hostility. Simply not being in a hurry changes a great deal.