"Well, if you were in this White House and you had seen the reaction in the public and in the press to the idea that Dan Quayle would be acting President for a few minutes during when they were going to give that shock treatment for the irregular heartbeat, I think probably if you were sitting in that White House, you wouldn't want to do that unless you had to."
Is it correct to say "during when"? What would it come close in meaning to?
Here you could say 'Dan Quayle would be acting President for a few minutes during the time when they were going to give that shock treatment ' or '...during the operation on...' or 'while they were operating on...'. The word 'during' must be followed by a period (say, 'the time when X') or an event (say 'the operation').