Despite the whimsically modern name, this construction has long been integral to English: I found three examples on the same page of Wycherley's The Country Wife (1675), for example.
That's a good one! I hate a man for loving you! If he did love you, 'tis but what he can't help; and 'tis your fault, not his, if he admires you. I hate a man for being of my opinion! I'll ne'er do it, by the world! (subject + VP, twice)
He afraid to lose you, madam! (subject + AP)
(In this earlier stage of English, the nominative was the default case, so 'I', 'he'; in Present-day English we would say 'Me hate' and 'Him afraid'.)
A construction consisting of a subject and a tenseless predicate, both topicalized, pragmatically used as an incredulous echo. The name (apparently coined by Adrian Akmajian) refers to the canonical example used as a catchphrase by Mad's Alfred E. Neuman: 'What—me worry?'. This has subject 'me', predicate the verb phrase 'worry'. (Since the construction lacks tense, the subject can't be assigned nominative case, so it takes the default case, which in English is accusative.)
Other examples, with context to show the echo pragmatics:
A: I heard John's a doctor now.
B: John a doctor, you must be kidding! (subject + NP)