Truman's win was unexpected for a reason. There were concerns until the 1948-1949 recession proved to be brief that the economy would slip back into a depression, so someone who could claim confidently that they were going to take Rooseveltian progressivism in a new, bolder direction would have had way more appeal than the middling, conservative approach Dewey chose to take. A more enthusiastic campaign would make all the difference, although Wallace still splits the progressive vote with Wilkie (and Truman for that matter) in some Western states.
President Harry Truman (D-MO) / Senator Alben Barkley (D-KY)
Activist Wendell Willkie (R-NY) / Governor Earl Warren (R-CA) ✓
Governor Strom Thurmond (SR-SC) / Governor Fielding Wright (D-MS)
There were several other factors in Truman's win in 1948:
1. Thomas Dewey was simply not likable. The reason was simple; he did not like people and he really couldn't hide it. His 1948 campaign was better than his 1944 campaign in that regard; he was a kinder, gentler Dewey, but not enough to defeat the more folksy Truman (who earnestly DID like people).
2. The Republican Party was split significantly. The convention that nominated Dewey and which authored the GOP platform was a group of moderates and liberals who were offering a rather liberal platform that was something of a New Deal Lite platform. The Republican 80th Congress, however, was a much more conservative body. Truman, in his acceptance speech at the DNC, challenged the GOP to enact their platform before the election, and promised he would sign it into law if they did. Truman was an astute pol and a nose-counter and he surmised correctly that the GOP Congress was too divided to enact the platform, handing Dewey a black eye of sorts.
Dewey was a lifelong Republican. Willkie, on the other hand, was a Democrat for most of his adult life who switched to the GOP in the 1930s. He was never fully in sync with the GOP and, after his defeat, spent the rest of his life as a man without a party. His support of FDR in WWII raised his approval level with the public, but made him less desirable to be nominated for President. FDR floated the suggestion that Willkie become a Democrat again, but we don't know if he was thinking it over because he died soon after that in 1944.
Willkie's defeat was not a close shave; he was beaten convincingly, and worse than he thought he would be. He was not like Al Gore, whom many Democrats would have preferred to Hillary Clinton in 2016 or Joe Biden in 2020, and his rival for the nomination would have been Bob Taft, who, whatever his politics, was a guy whom Republicans knew where he stood. Dewey, who was not a Taft Conservative, but who was, pretty much, a Business Republican, had trouble uniting the GOP in 1948; imagine the problem Willkie would have had getting the Taft supporters to join him, given that he was a guy who practically left the fold after losing in 1940.
I doubt that Willkie could have gotten that nomination. Had he been nominated, I doubt that he would have won. In
They Also Ran by Irving Stone, the author states that at no time during the campaign in 1940 was Willkie the man he was before or after the campaign. The campaign trail brought out the worst in him. He supported FDR's internationalist efforts, which were grudgingly supported by most of the GOP over time (even Bob Taft supported our entry into the UN). But, for different reasons, Willkie would likely not have beaten Truman. Willkie would have run on a similar platform as Dewey, and Truman would have been able to do the same by challenging the GOP Congress to pass something they loathed. And Willkie, for all his public regard, was never elected to anything. Dewey had a record in Government as NY Governor and Manhattan DA; he had a record of action and of getting things done. (Dewey was once viewed as the logical successor to J. Edgar Hoover as FBI Director.) Willkie had none of that, while Truman, with a mere High School education, had significant time in high public office.
Hmmmmm . . .
The Dixiecrats would have held the cards here. What would have happened?
The Dixiecrats would have immense leverage on Truman. The Thurmond/Wright electors were DEMOCRATIC electors; they were listed as the Democratic candidates in those states. They would likely have more leverage with Truman than Willkie. What concessions would they extract from Truman that would cause them to return to the EV fold? There would be little reason for the Dixiecrats to switch to Willkie. That's a real hypothetical. I suspect that they'd put Truman over the top in the end and take the position of "letting their Congressmen and Senators beat him down when he needs a beating" in the words of former Gov. Cameron Morrison (D-NC).