1919: An investigation into the Newport Sex Scandal finds complicity on the part of Assistant Secretary of the Navy Franklin Delano Roosevelt, forcing him to resign in shame. Democratic Presidential candidate James Cox, who is on the verge of choosing Roosevelt as his running-mate, suddenly changes his mind and chooses New York Governor Al Smith instead. Roosevelt's chances of a political career are shattered. Smith calls his complicity a "tragic dismissal of what could be tremendous potential."
1920: James Cox and his running mate, New York governor Al Smith, loose the presidential election to the Republican Harding/Coolidge ticket.
Same as OTL until 1928
1928: Herbert Lehman is elected governor of New York state. Smith looses the presidential election to Hoover same as RL.
Same as OTL until 1932.
1932: The presidential election appears to be a shoe-in for the Democrats. The only major candidates appear to be former New York governor and 1928 nominee Al Smith and Texan Speaker of the House John Nance Garner. Due to Tammany Hall-related scandals that rock Smith, Garner wins the nomination, but makes Smith his running mate. He runs to the right of Hoover in the general election, calling for corporate tax cuts, looser labor laws, and lower tariffs. In the end, Garner wins with 45% of the vote, compared 42% for Hoover, and 12% for Socialist Norman Thomas. Turnout is also very low. Without being appointed Secretary of Agriculture, Henry A. Wallace runs for Governor of Iowa and wins.
I didn't read the whole thing, because the scenario made no sense after this post, so I'll startr here.
Garner Reduces taxes & Tariffs back to Coolidge levels, and gets rid of Hoovers interventions in business. He also cuts back on the budget. (He basically does what Harding did after inheriting an economic mess from Wilson). By 1935 the countries economic health is restored, unemployment drops to 4-5%, and budget surplusses are the norm again. Garner is easily re-elected in 1936.