Deadlines are set in several ways some are artificial while others are real. In a situation where deadlines change frequently and rapidly it is important to be able to tell which are real and which are artificial. One must be flexible and agile with the ability to adapt to the needs of the office. A good attitude would be to imagine you are a juggler who must keep several balls in the air at one time. This would enable you to focus quickly on the job at hand and move on to the next without hesitation or stress. 

Employees who do not complete their required payroll forms make the payroll administrator's job more challenging. Asking this question allows the applicant to explain how she would handle this to ensure the worker still gets paid.

Tell us about a time when you missed a deadline.

(or)

Let's discuss a time when you missed a significant deadline.

If you answer something like "You never missed a deadline". Most interviewers will immediately conclude you are not experienced and may also feel you are lying. 

Approach - It is absolutely necessary to accept that you have missed a deadline and give reasons how you resolved and what you learned from it. This will demonstrate your experience.

You could say in one of the first projects earlier in your career you missed an important deadline and made the boss very upset. It was a great learning experience and after doing some introspection, you realized, you could have done better planning, prioritization and communication. Now, you use special tools, processes and methods to address these issues. Now your team, colleagues and management are always up to date so no surprises arise on meeting deadlines. 

Below are few things you may emphasize on in your response...

Effective planning

Procedural Improvements

Better Prioritization

Open communication

Better Status reporting