I've long thought that George Wallace would likely challenge President Humphrey in the primaries, playing on dissatisfaction with the liberal slant of the administration (run by two northerners) to form a base of support. How successful he would be would depend on the circumstances, but you have to remember that Wallace's populist appeal would help him immensely against Humphrey who was a politician not designed for the primary system. I could see him taking a few of the deep south states and picking up delegates in the northern rust belt states where he performed well IOTL, such as Wisconsin, Indiana, and Pennsylvania. The question is what he would do with his delegates; I think he'd look to wrangle some concessions, both personal and political, from Humphrey in exchange for not making a big fuss at the convention.
For the Republicans, I think Reagan is an obvious choice to run. Governor Rhodes of Ohio would be another solid option without the taint of Kent State on his record. Nelson Rockefeller would run because after chasing the nomination for 12 years he just wouldn't be able to resist another go at it, although he'd be about as skilled at running in the primaries as Humphrey and without the benefit of being a sitting president. Assuming he still wins, which he should, Senator James Buckley of New York would provide a conservative alternative if Reagan decides to hold out until 1976, and Peter Dominick of Colorado might do the job if neither of those options runs. John Volpe was on Nixon's short list for VP, and might make a go at the big job himself as a moderate.
Now for the list of Republicans who I think would not run. Edward Brooke is up for reelection and never showed any interest in seeking the Republican nomination for president. Even if he did, his campaign would not get very far in 1972 when the prospect of the first black president would not have been a selling point. Howard Baker, too, is up for reelection in 1972 and didn't yet have the stature to run a national campaign. On the liberal Republican bench I doubt you'd see either George Romney or John Lindsay make another attempt. And Gerald Ford had no interest in the job until he was thrust into it upon Nixon's resignation, so I think he'd be content staying put in the House.
At the end of the day I don't know that it's impossible that a Republican could beat Humphrey even if the economy was good and the war in Vietnam didn't end in the collapse of the South. There's still going to be a lot of discontentment among traditional Democratic voting blocks in the south and the west that might allow someone like Reagan to win in a squeaker come election day.
