Unlikely. The Depression had pretty much had gotten as bad it could get by 1932, and some kind of recovery was inevitable. Many of FDR's best programs in the New Deal were already been pushed and would have been enacted without him.
You would need continual stagnation for several years, plus an incompetent President, to get to the point where the American people would lose confidence in constitutional government. Even then, it is unlikely any US President could have seized power without Congress being compliant. It's hard to see how anyone so inclined could get the nomination in either party.
There is zero chance of a military coup. The US had an extraordinarily small armed forces in the 1930s, and most generals prized themselves in being apolitical. At most, you might get a handful of senior officers who would cooperate in a larger plot to seize power.