It’s a bit of a setup, but I’ll highlight the big part:
1) JFK and LBJ are elected to the senate much earlier (1947/1941, respectively)
2) They win the 1956 presidential election. (LBJ/JFK)
3) They trade places in 1960 (JFK brings up his Addison’s disease, and LBJ agrees because they get along)
4) Dallas still happens (Don Yarborough’s governor)
5) LBJ selects RFK as his running mate in ‘64 (both because Rockefeller is the nominee, and LBJ and RFK get along better than IOTL)
6) No Korea/Vietnam
7) Nixon was never Senator (he’s a behind the scenes powerbroker trying to wrest the party away from Rockefeller-Romney)
8) After more than a decade of trying, he’s the ‘72 nominee (dog that caught the car)
9) He pulls the same stunts from Watergate, except in the public sector
10) Jimmy Carter (elected Governor and US Representative in 1966) is RFK’s VP
11) RFK, not wanting to deal with Nixon’s ratfucking, decides that if he wins the election, he’ll refuse to swear in, handing the Presidency to Carter on day one.
12) RFK wins in a nail biter, be announced that he won’t serve as president for 4 more years (something about it not feeling right to serve longer than his brother.
13) Nixon’s ratfucking comes out, and now Carter has to deal with prosecuting Nixon. (No Chennault affair, but all the other things from the White House Plumbers show on HBO like the stuff with Dita Beard and hosting the RNC in San Diego stuff happens and is prosecuted.) (Maybe she grows a conscience or realizes Nixon won’t win, so there’s no use going down with him.)
This gave me ideas for 2 TLs, one focusing mostly on Carter’s prosecution of Nixon (and what a ‘73-‘81 presidency could look like), and the other a much broader scopes TL where a successful Carter gets to shape the presidency and the Democratic Party much more than IOTL, and so you get the following presidencies: Carter ‘73-‘81, Michael Harrington (as a leftist backlash against Carter’s centrism) ‘81-‘85, Bill Blythe III (Clinton IOTL, and a return to Southern Moderates) ‘85-‘93, Al Gore ‘93-2001, and Ted Turner ‘01-‘05.)