The Great Society would have been a tougher nut to crack. However, Nixon not only failed to take any action, but facilitated Federal expansion, establishing the EPA, OSHA, imposing the first wage and price controls in peacetime history, and recognizing Red China.
First, Taft would have had to get elected. He wasn’t a popular war hero, like Eisenhower, and would have been subject to low attacks from Democrats that didn’t affect Ike’s campaign.
Secondly, he would have had to win Congress. Taft didn’t have the coattails Eisenhower did. The Taft-Hartley Act was a big bugaboo for labor unions and they would have gone all out to beat Taft.
Third, if Taft tried to repeal the New Deal he would have lost some Republican votes in Congress and wouldn’t have picked up as many Southern Democrat votes as you think. At that time, Southern Democrats were “conservative” in terms of not wanting more big government, but not conservative in terms of wanting less government. They had been elected with FDR. They voted for him. Their constituents had voted for him. Were they really going to vote to repeal TVA, Social Security, the SEC, FDIC.
Fourth, Taft would have had to live. He didn’t last out the Summer of 53. Whether he knew it or not he was dying, so maybe Eisenhower did Taft and his family a favor.
Fifth, what does it really mean to repeal the New Deal?