You are making the mistake of thinking that is possible to spend our way out of depressions. Germany got out of the depression because real wages were held down. Roosevelt, by contrast, kept propping up wages and prices which equalled continued depression.
Maybe because one quarter of the country was out of work and those still working still had to eat and put a roof over their head. Maybe in the long run depressing wages may have caused the recovery to move slightly faster, but as one of Roosevelt's advisors told a Congressional Committee, "People don't eat in the long run, Senator. They eat every day." And that took money.
You also forget that Hitler had dictatorial powers and didn't have to worry about a congress or a Supreme Court. Hitler achieved his recovery through a massive rearmament program, something not open to Roosevelt, but also through extensive public works projects and also work creation programs. There was the Labor Service and other government programs. And Jews and women were excluded from the work force as well, don't forget the impact that had on unemployment.