First off, one or many people are probably mad if it is a high priority item.
It is easy to:
- Blame others.
- Talk about how the deadline was unfair (now after it's too late) or how circumstances changed.
- Provide excuses.
The question that can really help is one that may seem counter-intuitive to "excuse-providers" .....
"How did missing this deadline affect you personally?"
This does not have to be the first question, and maybe it should not be, but it needs to be asked. Also, if it affected more than one person, you will have to ask it more than one time! (Because most everyone will have a different answer.)
What this question may do:
1.) Right away it shifts the attention to where it should be - the impact. By asking that question, you are telling the other person you care because you want to know what this (missed deadline) has caused.
2.) It makes it personal and while people understand organizational impact, they "feel" personal impact much more easily. In short, the question is a sign of empathy.
3.) It shows a willingness to want to solve the issue. Before you can do that you need to know the issue (which may be bigger now that a deadline has been missed). So, it boldly inquires about where you are now (and does not try and sweep anything under a rug.)
4.) The answer to the question may open up new possibilities .... How do we adjust now? What can be done, salvaged, etc.?
5.) It shows you want to LEARN from the event. It shows ownership not just in the specific deadline missed but in working forward to ensure it does not happen again. You can work with their answer in making changes going forward.
Hopefully you will never miss a deadline in your life again, but chances are we all will. Can this question really "do" all those 5 things? Try it.