WI Nixon Flips Illinois and New Jersey in 1960 and It Goes To The House?

Illinois had a margin of roughly 9000 votes and New Jersey a margin of roughly 22000 votes. ITTL only these are the changed states from OTL. Byrd will decide this one with his 15 electors. Who is most likely to win this one? Could Nixon somehow win this (IMO this is not plausible but I am not too knowledgeable on Nixon)?
 
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