How could the neocons have stayed Democrats?

No Vietnam. It tore the Party apart on foreign policy grounds. Without that, there'd likely still be disagreements within the Party on those same lines, but they wouldn't be so urgent as to drive the Scoop Jackson types (albeit not the man himself) into Reagan's arms.
 
What would it have taken to keep the neoconservatives in the Democratic Party?

Scoop Jackson is elected president in 1976. Very unlikely, I know. Still, if Carter had not run, Jackson just *might* have won the FL primary (which in OTL was Carter, 34.52%, Wallace, 30.52%, Jackson 23.91%) and later PA (Carter 36.95%, Jackson 24.57%) and after that who knows, especially if a lot of liberals had divided the left-of-Jackson vote among themselves? https://en.wikipedia.org/wiki/Democratic_Party_presidential_primaries,_1976
 
Scoop Jackson is elected president in 1976. Very unlikely, I know. Still, if Carter had not run, Jackson just *might* have won the FL primary (which in OTL was Carter, 34.52%, Wallace, 30.52%, Jackson 23.91%) and later PA (Carter 36.95%, Jackson 24.57%) and after that who knows, especially if a lot of liberals had divided the left-of-Jackson vote among themselves? https://en.wikipedia.org/wiki/Democratic_Party_presidential_primaries,_1976

BTW, it should be noted that although Jackson was the neocons' first choice in 1976, some of them did hold out hopes for Carter--after all, he was from the traditionally hawkish South, and on foreign policy he had attacked Ford from the right as well as the left. But after his election they presented him with a list of candidates for jobs, and were terribly disillusioned by the outcome--Peter Rosenblatt got a job as an envoy to Micronesia, and that was it. As Elliott Abrams put it, "We got one unbelievably minor job. It was a special negotiator position. Not for Polynesia. Not even for Macronesia. But Micronesia!" https://books.google.com/books?id=RME4nM0SAF4C&pg=PA175
 
BTW, it should be noted that although Jackson was the neocons' first choice in 1976, some of them did hold out hopes for Carter--after all, he was from the traditionally hawkish South, and on foreign policy he had attacked Ford from the right as well as the left. But after his election they presented him with a list of candidates for jobs, and were terribly disillusioned by the outcome--Peter Rosenblatt got a job as an envoy to Micronesia, and that was it. As Elliott Abrams put it, "We got one unbelievably minor job. It was a special negotiator position. Not for Polynesia. Not even for Macronesia. But Micronesia!" https://books.google.com/books?id=RME4nM0SAF4C&pg=PA175
lol
 
Top