I vote in favor of the question mark, inside quotation marks.  How would the
sample in question differ in structure from a quote introduced by "he said,"
or "he asked"?  Such would also form complete sentences in themselves, the
quotation itself functioning as the direct object of the larger sentence,
wouldn't they?
My question comes directly from a grammar worksheet.  In the sentence, "The
treasure is worth two million dollars," what part of speech is "worth"?  The
answer key labels it as a verb.
Janet Master