Well um uh I- I understand Newt must be very angry
and I- I don’t exactly understand why, but uh
look, I wish him well, it’s a long road ahead,
i- he's a good guy, I like he and Callista, and uh-
uh we got many months ahead of us, so
uh I’ll leave it at that [laugh].
For some background, see "Patterns of Prestigious Deviance", 10/1/2011; also Philipp Angermeyer and John Singler, "The case for politeness: Pronoun variation in co-ordinate NPs in object position in English",Language Variation and Change 15, 2003; and Frank Parker, Kathryn Riley, and Charles Meyer, "Case Assignment and the Ordering of Constituents in Coordinate Constructions", American Speech 63(3) 1988; Graham Shorrocks, "Case Assignment in Simple and Coordinate Constructions in Present-Day English", American Speech 67(4) 1992; Frank Parker, Kathryn Riley, and Charles Meyer, "Here us go again", American Speech 69(4) 1994.
My own intuitions, for what little they're worth, give a funny result in this case: "I like he and Callista" feels like an instance of hypercorrection; but "I like him and Callista" feels like something that the neighborhood prescriptivists are going to glare at me about.