IOTL, Democratic candidate John F. Kennedy went against his brother's advice and picked a southerner, Lyndon B. Johnson, to be his running mate. However, Bobby Kennedy wanted his brother to pick a labor-friendly liberal, namely Walter Reuther. What if Kennedy listened to his brother's advice and picked Reuther to be his running mate?
This would be a disaster. The Democrats' association with "big labor" was a liability in the South and even in much of the North (the fact that a heavily Democratic Congress passed the Landrum-Griffin Act should indicate that organized labor was hardly universally popular even among Democrats) and Reuther, despite his anticommunism, was considered left-wing even by some people in the labor movement. ("Don't call him Reuther," [Steelworkers Union leaderDavid J. ] McDonald told his aides. "Refer to him as that no good red-headed socialist bastard Reuther."
https://books.google.com/books?id=ghy45fyXYyoC&pg=PA336&lpg=PA336 McDonald was one of the few union leaders not to object to JFK's choice of LBJ as running mate.) A former Socialist Party member who had worked in a Soviet factory in the 1930's is not going to help the Democrats with the median voter. You can immediately count on the Democrats losing Texas and the Carolinas and Louisiana (where as it was the state Democratic committee came close to endorsing a slate of pro-Harry Byrd electors instead of JFK, even with Johnson on the ticket) and Missouri and New Mexico (where there were still a lot of conservative pro-LBJ Democrats in "Little Texas") and Nevada (another state with a lot of conservative Democrats). Even in northern states which JFK narrowly carried, like Illinois, I think he would be a net liability. Yes, his civil rights position could make him popular with African American voters, but they overwhelmingly backed JFK anyway. JFK's Catholicism was already enough of a handicap in downstate Illinois, and Reuther would be a further burden there.
The idea is so politically senseless that I would question that Bobby seriously expected his brother to go along with it. The only source for Bobby's having pressed for Reuther that I can find is the photogrpaher Hank Walker.
https://webcache.googleusercontent..../time.com/3491219/+&cd=12&hl=en&ct=clnk&gl=us I would simply have to question Walker's account. Yes, Bobby liked Reuther--he found him a refreshing contrast to corrupt labor leaders like Hoffa and Beck--and disliked LBJ. But if he wanted to stop LBJ, there were a lot more plausible candidates than Reuther--Scoop Jackson (who could appeal to labor without being seen as left-wing), Stuart Symington (a border-state moderate liberal who was everyone's second choice for president), Albert Gore (if you want a non-LBJ southerner), Minnesota Governor Orville Freeman (to appeal to farmers) etc. Even Humphrey, though unpopular in the South, would be less controversial than Reuther. Bobby was sophisticated enough to know you could be a social democrat like Reuther and still anticommunist, and that even though Reuther was in fact an ally of the CPUSA in the 1930's, those days were long gone--but surely he was also sophisticated enough to realize that ordinary voters might not get these distinctions. If he really did press for Reuther as JFK's running mate, all I can say is that this was a crazy proposal JFK was most unlikely to approve.
BTW, according to Arthur Schlesinger, Jr., Bobby did not object to JFK's inital choice of LBJ because he thought it was merely a pro forma offer--LBJ would never accept! When LBJ astonished both brothers by accepting, Bobby tried to talk LBJ out of it, but in vain. Bobby said to James Rowe, " My God , this wouldn't have happened except that we were all too tired last night. Don't you think this is a terrible mistake? Don't you think Stuart Symington should be the candidate?"
https://books.google.com/books?id=SLPqDwAAQBAJ&pg=PT192 That sounds a lot more plausible to me than his saying that about Reuther. It is possible in the frantic late-night conversations between the brothers about what to do about LBJ's acceptance, Bobby did raise Reuther as a possibility, but I just can't see him as a serious prospect.