JFK had enough electoral votes to win without Illinois' 27 E.V.s.
The final electoral tally was 303 to 219 in favor of Kennedy.
After the absentee ballots were tallied, Nixon actually had the 32 electoral votes of California. Yes, that ship has long since sailed and though I'm not Harry Turtledove, I can't help but wonder how much better America here in 2014 would be had Richard Nixon won.