1976 Carter: ironically despite this being a winning candidacy Carter was up like 30 points on Ford the summer before the election. Ford closed the gap to 2 points on election day. Many pundits have concluded a few more days campaigning and moderate Ford would likely have won this one.
I was in a poli sci course that semester and the course was almost entirely about that election. The data we saw suggested that Ford peaked the weekend before the election, so had it been held on Sunday instead of Tuesday he might have been retained in office. We also astonished the professor by predicting that the election would be one of the closest of the century, which it was.
I'm inclined to think the race was going to tighten no matter what because there too many things in the incumbent's favor, so I'm hesitant to say Carter '76 was the worst winning campaign.
Wildcard choice for worst winning campaign: Clinton '96. He had peace, prosperity, Democrats had only held the WH for one term, had a washed-up, inept campaigner for an opponent, had a GOP Congress to rail against...and yet still won only by single digits and couldn't crack 50% of the vote. I know there were questions about his character, but were they any worse than questions about Nixon's character when he won in '72? I guess also we could see the beginnings of regional polarization in this election..
There was also the Ross Perot factor possibly keeping Clinton 50%.