In the pre-war era, roads weren't everywhere. Rural folks in North Texas and Western Oklahoma, upon being ignored by the capitals of their respective states, opted to push for a new state that would focus on infrastructure in their region: Texlahoma (creative, I know). Sitting Vice-President John Nance Garner was a supporter of the idea.
So let's say Zangara is successful and President Garner takes up the cause of Texlahoma! Alternatively, Garner convinces Roosevelt that it's a good idea to push for it. With Presidential support, the secessionists are successful and the US gets one more boxy low-density state. Hurrah!
What now?