On this topic, I really do not think enough people appreciate (A) how close a lot of the Southern states were but (B) how concentrated Reagan's victory margins were in Southern suburban counties that were simply not as populous in the days of the Solid South:
Look at how much of the rural South stuck with the Democrats, and yet the only "Southern" states Carter won were his home state of Georgia and West Virginia. These wins for Reagan are super close, too:
Tennessee: 48.70% GOP, 48.41% DEM
Alabama: 48.75% GOP, 47.45% DEM
Arkansas: 48.13% GOP, 47.52% DEM
Kentucky: 49.07% GOP, 47.61% DEM
North Carolina: 49.30% GOP, 47.18% DEM
Mississippi: 49.42% GOP, 48.09% DEM
South Carolina: 49.57% GOP, 48.04% DEM
Only Texas, Oklahoma, Florida and Virginia were really out of reach. Carter also almost won Massachusetts, even with Anderson. A very minor shift could have given us this map:
EDIT: This post made me think of a funny memory from college. I cannot remember the class, but our professor was kind of glossing over politics in the 1980s, and he put up a county map of the 1980 election, more or less just to show that Reagan won handily. I was already an Atlas nerd by this point, so I laughed when he said something to the effect of, "As you can see, Carter only won a handful of states in the Deep South, and Reagan won pretty much everything else." Without a state by state map, that assumption is very easy to make.