At some point in any person's career, the inevitable happens and an important deadline needs to be missed. With your interviewer fully understanding this fact, they are solely interested in how you react to this situation and what you do to make the situation right. In your answer, focus on the refocused planning and communication needed while also avoiding blaming others for the situation. Your interviewer holds accountability as a desirable virtue, so be sure to take accountability for actions in your response.
"In my current position, I am very used to handling multiple tasks and projects on a day to day basis. Last year, my team was tasked with what started as a low priority project. After assembling a team to initially discuss the details and set a deadline for completion with our management, the project unfortunately fell off the radar of everyone on the team with many more high priority projects coming up each week. As the initial project's deadline was within a week of being due, our CEO reached out to me for a progress report. I immediately took full responsibility for letting this fall off the radar and I ensured our CEO that we would have an updated timeline set by the end of the week. In doing this and completing the project to his satisfaction, this was really the tipping point in our department moving forward utilizing a detailed project management tracking system. To this day, I can't say enough about how appreciative I am about utilizing this awesome system. Moving forward, you can rest assured knowing that I take full accountability for my actions and do what is necessary to communicate new expectations and meet them fully."
"Having been in this situation before, I would first sit down to gather all the facts possible in the situation. What was the deadline, why wasn't it met and what can be done are all important questions moving forward. From there, communicating to all key parties is extremely important and doing so in a timely manner is critical. In this communication, taking accountability and setting new expectations for delivery in a concise and tactful manner will most often put stakeholders at ease and allow for successful completion."