Start off by telling the interviewer that you are typically an organized person and achieve everything on time. Share how you usually organize your work. You might share that you keep a to-do list of all the objectives that you must complete, keep your electronic calendar up-to-date and that you spend 5-10 minutes at the beginning of your day reviewing your calendar for the day as well as prioritizing your to-do list for that day.
Next, share a time when you failed to get an assigned task done on time due to something outside of your control. Perhaps you were sick, an emergency arose, or someone else called in sick for the day changing your priorities. Share how you prioritized your time with the goal of achieving the deadline, and share why you were not able to achieve it on time. Finally, be sure to wrap it up by reiterating that you are usually a deadline driven person, and you almost always complete everything on time.
"I am always diligent when it comes to deadlines. However, once I remember having an abnormally large order from a regular client once. I was a little stressed about making sure it was perfect, so I put in four overtime hours to meet the expectation. It felt great to deliver high-quality service."