Humphrey wins 68, who runs in 72?

Honestly, Humphrey would probably lose on the account that the democrats have ad 12 total years in office with 3 presidents and Vietnam will be an issue. If Humphrey deals with that well enough, he could win. But Humphrey will have to throw a long ball in ‘72.
 
Most likely POD for HHH in 1968 is imo Reagan getting it because Nixon decided to play the long game and wait till 72 or 76.

My guess is you get a few potential scenarios 1) HHH wins in 72, gets to set things up for Muskie or Carter in 76 2) HHH wins in 72, but things get botched enough you get a republican(Reagan/nixon/bush your choice) in 76 2) Nixon wins in 1972("Third time's the charm for Tricky Dick...).

The least likely but theoretically doable one would be Reagan in 1972 with it's own variations -- On one hand you have expanded welfare(UBI, UHC, more generous than OTL EITC), vietnam being a stalemate, 4-6 liberal justices on the SC with resuting court cases, expansion of busing for 4 more years causing a backlash. OTOH there's the fact that Reagan's going to be elected in stormy waters, so either 4 or 8 years of him with the end results being as I keep mentioning weaker movement conservatism -- someone did a thread on 1968 Reagan on here with that result but i forget who.
 
Reagan for sure, probably Rockefeller and maybe Agnew if his scandals haven't caught up to him yet. Then there's people like Romney, who might do better with Vietnam presumably being less of an issue, and Connally, depending on how Humphrey's term goes.
 
If you flip OTL Republican, states of:
California (223,346 votes, 3.08%)
Missouri (20,488 votes, 1.13%)
New Jersey (61,261 votes, 2.13%)
Ohio (90,428 votes, 2.28%)

The results gives Hubert Humphrey a majority and making the map look like this:
1968.png
 
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