There are major differences. Notably, the fascists were open to nationalization of industry and economics for the benefit of the state (a feature of their ideology as well being that the state is supreme) fused with Keynesianism, whereas the New Deal was simply Keynesian reform which was not purposed to harness the individual for the benefit of the state, whether that being the economic barons or the government. The New Deal was for the benefit of the citizens (a "New Deal" for the American people; not the American government).
Both fascist economic reforms and the New Deal looked to Keynesian economics, however the fascists were happy to take government control of certain industries if not all and the fascists believed in authoritarianism and hated Liberalism and Democracy because they saw it as weak. New Dealers were firmly based in democracy and did not believe that the state was almighty or republic weak and on its last legs as the fascists did.
Fascism evolved out of a slew of ideologies, both left and right. However, in the end it was undeniably a hard right ideology and again, the New Dealers were based in Social Liberalism. The Fascists absolutely hated Liberalism. The first people Hitler sent to the death camps before even the Jews were the liberals, socialists and communists. Mussolini hunted down liberals and socialists with all his might. These are people who are not going to like each other.
I can see Huey Long breaking off Louisiana at least. He may have supported populist economics and a more dictatoral government, but it was for the people and was more of an odd American Communism than Fascism.
Currents within fascism would link the state and its desired people collectively, so your point here is lost on me. The trappings of democracy are always nice, but how democratic can a government be that redistributes money from its treasury to sections of the masses strategically?
Such a regime is democratic in the sense that its leaders are elected, and its people may seek office, but like the fascist state, it risks severely damaging the liberty of individuals within the society. Even the U.S.S.R. was nominally democratic, but regard for individual liberty was something it long lacked.
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