In any case, the conservative coalition in Congress would move to repeal the New Deal and move back to laissez-faire governance as soon as WW2 ended. IIRC Truman only saved the New Deal IOTL by saying to the conservatives 'okay, if you don't like the New Deal, I'm going to institute single-payer healthcare, repealing Taft-Hartley, all that stuff, and if you disagree I am going to take it to the American people and see how they like it'. While he didn't get any of that through Congress, it did ensure that they wouldn't repeal the New Deal from that point onwards.
Now, Vandenberg wouldn't do anything like that (mainly because he was a conservative) but Dewey might have. IIRC Dewey and Truman weren't too ideologically opposed from one another, but Truman was probably the better politician of the two of them, hence why he won in 1948. With that said, if Dewey were able to politic his way into keeping the New Deal without any concessions, he'd likely win in 1948 and give way to Eisenhower in 1952. If Vandenberg repealed the New Deal, or Dewey ended up conceding the New Deal to the conservatives, Truman would likely run full-force on a social democratic platform and win 1948 in a landslide.