I had to look up who Jimmy Carter was, but was somewhat surprised to find out that he finished second in the 1976 Democratic primaries, and came within 2% of beating Udall in the New Hampshire primary. I guess if he had won both in New Hampshire on top of his Iowa Caucus victory, he well could have been the nominee. Ironically, in 1984 he came within 2% of winning the New Hampshire primary again but at this point he had been Vice President, was no longer a dark horse, and his campaign fizzled afterwards.
Could Carter have beaten Ford? Udall won the following states by a low enough margin that I could see Ford carrying them due to a relative lack of support for Carter outside of the former Confederate states:
Ohio 0.1% 25
Arizona 0.2% 6
Nevada 0.2% 3
California 0.3% 45
South Dakota 0.5% 4
Maine 1.4% 4
Wisconsin 1.9% 11
Oregon 2.0% 7
Hawaii 2.7% 4
New Jersey 3.0% 17
Washington 3.1% 9
Pennsylvania 3.2% 27
That is 172 electoral votes.
Udall carried Arkansas by 3% of the vote, Missouri and Louisiana by less than 1% of the vote, and Maryland by 3%, but I assume Carter would have carried all three states.
In terms of Ford states, Carter would have picked up his home state of Georgia, where the Udall/ Carter ticket fell short by only 4%, and I can see Carter taking Kentucky (Ford by 2%), North Carolina (Ford by 5%), and Texas (Ford also by 5), but none of the other southern states were really that close. That is 60 electoral votes.
The only way I could see Carter doing it would be with a Carter/ Brown ticket and he somehow still carries California, as well as Washington, Pennsylvania and New Jersey. Give him Georgia, Kentucky, North Carolina, and Texas and the EV becomes very close, even with losing Ohio and Wisconsin. And I'm not sure how well a Carter/ Brown administration would be received in Washington.