Backing of the military doesn't matter that much - Hitler didn't have it when he actually took power, and was relying on the SA for most of his muscle when he needed it. Successfully imposing that sort of rule only works when it is done fast, because doing it slow virtually always allows people the chance to stop you. Most countries had fascist movements in the 30s and 40s. Most of those movements failed because they never got the chance for a knockout blow.
Note that all of the successful fascist takeovers relied on very weak institutions. The Second Spanish Republic only came to power in 1931, and almost instantly began pissing everybody off. That helped create a legitimacy vacuum as well as a stability one, which gave Sanjurjo's cabal an opening to move. The Weimar Republic was formed after a series of revolutions following the defeat in WWI - none of the various factions had the legitimacy previously enjoyed by the House of Hohenzollern, most of the disparate groups behind them hated one another, and the state they set up was fundamentally unstable as a result. This resulted in a legitimacy vacuum as well as a stability one, which gave Hitler's cabal an opportunity to move. Italian fascism was spurred by public discontent with Italy (an Allied Power!) being left out of much of the spoils of WWI and poor treatment by the Allied Powers as a whole, combined with poor economic performance and a growing lack of confidence in the Crown. This helped create a legitimacy vacuum as well as a stability vacuum that gave Mussolini's cabal a chance to move.
In France, Britain, the US (the other Great Powers of the era)? All had fascist movements. None were taken over because the institutions were strong enough that the "Only a Strong Man can guide us from this dark time, I am that strong man, I now rule entirely!" moment never came.