I suspect the phrase originated with his book "The Innocents Abroad", in Chapter 27:
"There is one remark (already mentioned,) which never yet has failed to disgust these guides. We use it always, when we can think of nothing else to say. After they have exhausted their enthusiasm pointing out to us and praising the beauties of some ancient bronze image or broken-legged statue, we look at it stupidly and in silence for five, ten, fifteen minutes--as long as we can hold out, in fact--and then ask:
"Is--is he dead?"
That conquers the serenest of them. It is not what they are looking for--especially a new guide. Our Roman Ferguson is the most patient, unsuspecting, long-suffering subject we have had yet. We shall be sorry to part with him. We have enjoyed his society very much. We trust he has enjoyed ours, but we are harassed with doubts."