It's not a completely horrible question. I can imagine it drawing out the candidate's beliefs about process improvement, prioritization, deadlines etc.
I would use it as an opportunity about how I think work should be prioritized (Asking the hypothetical boss whether they communicated that this was the most important thing to them). Also, I'd talk about my beliefs about continuous improvement (Adding this situation to my hypothetical retrospective board so we could make sure it doesn't happen again). I'd also use this as opportunity to discover what they would do about an unreachable deadline.
The thing is, these are my talking points, rather than a direct answer to the question. They're personal to me. Rather than just providing a witty answer, I've moved the conversation to the things I want to discuss. The things that advertise me, and things I want to discover about my prospective employer.
You've asked this questions because you see interviews as a series of questions you have to pass. They're not, or at least they shouldn't be. In the end, they'll hire the person who communicates that they're the best candidate, not the person with the snappiest answers. Write down the things you'd like to communicate in your next interview. Then look up some common interview question and practice "hijaking" the conversation.