President: Kennedy wins by 0.52 (50.26/49.74)
Governor: Dalton (D) wins by 16.06 (58.03/41.97)
And here's the swing map for the difference between Kennedy's percentage and Dalton's percentage
Dalton (D-Kennett) did get a higher percentage in some of SEMO due to his roots there. But Dalton won Reynolds County by 28 points and Nixon won there by 4 points. LBJ carried Reynolds County by a 78/22 margin.
As we can see here, there was a heavy anti-Kennedy swing in the Presidential results from 1956 to 1960 in some parts:
So yes.. the number of anti-Kennedy Democrats in Missouri is.. interesting.