more than he cared about the way most Americans struggled and lived their lives.
Richard Parker's book John Kenneth Galbraith: His Life, His Politics, His Economics has some interesting things to say about Stevenson.
On page 256 he writes about James Loeb and George Ball having dinner with Stevenson in an effort to recruit the popular governor to run for president. At the dinner they discovered that Stevenson didn't believe in Truman's Fair Deal (he outlined his objections point by point), opposed federal funding for public housing, opposed repeal of (anti-union legislation) Taft-Hartley, that he would risk strikes to stabilize the economy, that federal funding for education should be used only as a last resort, opposed Truman's health care reform (calling them "socialized medicine"), and he though civil rights was a matter for states to address, and not the federal government -- all of which disturbed Ball and Loeb.
http://www.amazon.com/gp/reader/0226646777/ref=sib_dp_srch_pop/002-7593254-8792836?v=search-inside&keywords=adlai&go.x=0&go.y=0&go=Go%21#Revealing the source of Stevenson's lack of committment to progressive princinples, on page 316 Parker writes about Stevenson's anger at a Kennedy speach attacking French colonialism in Algeria. Stevenson was more content to advance his clients' interests in Ghana, the Belgian Congo, and South Africa (he was a corporate lawyer at that point representing the interests of the multinational corps that made so much money exploiting cheap labor and resources in Africa) than he was in social justice.
http://www.amazon.com/gp/reader/0226646777/ref=sib_dp_srch_pop/002-7593254-8792836?v=search-inside&keywords=adlai&go.x=0&go.y=0&go=Go%21#So, the answer to your question, I believe, is that it would have been very difficult for Stevenson to have been a good president in the eyes of anyone who liked the New Deal, progress and justice.