If by chance you do find yourself stumped, there is NO harm in saying, "I'd like to think about that for a second" - and then think through your answer. While you can't take all day, obviously, you can take a couple of seconds to sort out your thoughts - which could make all the difference in your answer.
And have questions for them. Interviewers love that. Ask the interviewer how they interpret the school's mission; if the school has some sort of tag line (ours is for the whole university - "The difference is Duke") ask them what they feel that means (I asked my interviewer, who ended up being my adviser, what she felt the Duke difference is). You're showing interest in the school and its faculty by being curious about them.
Something else I did. Duke had 200 apps for 56 slots. After my interview, which was when I realized I wanted to go there more than anything in the world, I went out and got thank you notes and wrote a short one to my interviewer, thanking her for her time and closing with "I look forward to seeing you on campus in the fall" - the same type of note you should send after a job interview
. I went a bit farther...I spent a bit more and bought Crane paper notes (the watermark is quite distinctive; I used to do my resumes in Crane paper and it NEVER went unnoticed or unremarked upon by the person interviewing me) edged in Duke blue, with envelopes lined in Duke blue. Best $12 I ever spent...I think it's perfectly acceptable to thank an interviewer - basically, it IS a job interview after all - and I'd be willing to bet you'd be one of just a few that would think of such a touch. Send that thank you note (NEATLY NEATLY handwritten and in ink!) WITHIN TWO DAYS OF THE INTERVIEW, and not one moment later. Send it the very next day or even the same day if you can. Do this even if you have a phone interview.
Just my own two cents. GOOD LUCK and keep us posted.