I'm surprised there isn't more love for Edmund Muskie in this thread, as he seems like one of the more plausible cases to go from failed VP nominee to POTUS. Off the top of my head, you just need a few things to happen. First, someone needs to come in during the lead up to the 1972 election, hit him on the back of the head, and tell him that running in primaries is going to be different than anything that he's dealt with before or up to this point. He'll need to hire a campaign staff that reflects the new reality of campaigning for the nomination. Second, he needs a stronger response to the Canuck Letter and political attacks in general. That should be sufficient to get him the nomination that year.
I don't know that he can defeat Nixon in '72 without significant changes, but it's certainly likely that he will make the race more competitive. My thought is that if he loses a bitter election to Nixon, having been on the receiving end of the President's dirty tricks, he might take a more active role in bringing down Nixon which would keep his name front-and-center for 1976. The results of the Watergate scandal would show that Muskie had been more or less cheated out of the presidency by chicanery, and that is a wave he could ride right through 1976 and into the White House.
I too have a soft spot for Muskie. Unfortu-
barely, with hindsight- & of course too late
to help Muskie- 1972 IOTL was exactly the
wrong year for him to run. Democratic Party
voters that year were in a agitated, even
angry, mood. Muskie's campaign rested on
the premise that voters should trust him, a
pitch that they felt too vague & insufficent
(especially when McGovern was running to
Muskie's left on a firm anti-Vietnam War
platform, a conflict Muskie had previously
been in favor of). By 1976 IOTL, by contrast,
with the war over & Nixon out of office, the
voters had calmed down & were instead
looking for reassurance. So they voted for
Jimmy Carter whose pitch, as noted colum-
nist Jeff Greenfield pointed out, was "trust
me"- the same approach Muskie had used
four years earlier(SEE Greenfield's book THE
REAL CAMPAIGN, 1982). If this worked for
the previously unknown Carter in 1976 IOTL,
maybe it might have have worked for Muskie
(who @ his best was called "Lincolnesque" as
witness IOTL his famed broadcast opposite
Nixon on the eve of the 1970 Congressional
elections). In politics, as in so much of life,
timing can @ times be everything.