Neither candidate does well with the deep south. Without a conservative, the Goldwater states go for Unpledged Delegates. My guess would be either writing in Barry Goldwater, Strom Thurmond or George Wallace.
LBJ still wins however Dirksen manages to hold most of the solid Republican states like Northern New England and the Rocky Mountain states. Scranton wins Pennsylvania for Dirksen. Dirksen in the end loses for two reasons. One is his age, 67. Two is the fact that 1964 was simply a Democratic year.
I'm probably being too generous to Dirksen but who cares...
Johnson: 320
Dirksen: 171
Unpledged: 47