How did the democratic regimes of Britain, France, and the United States avoid totalitarian takeovers while the Weimar Republic was unable to?
The Weimar Republic, the republic established in 1919 to replace the Kaiser's Empire, succumbed to totalitarianism because World War I did tremendous damage to the country and its nationalism, whereas nationalism was heightened in other countries. When the treasury was unable to meet French reparation payments and France invaded the Ruhr, triggering hyperinflation on newly printed currency, unrest and desperation escalated. Of all the right-wing parties that developed as a reaction to situations and unrest, the Nazi party had a great influence because of Hitler's popularity, thanks in part to Mein Kampf, and because the pro-democratic parties didn't fare well after Stresemann's death. All these factors--different from the experiences in other countries--left the Weimar Republic primed for totalitarianism.
They were not invincible to the pressures that affected the Weimar Republic either, there was a significant fascist movement in Britain and France before the war and a German-American Bund in the US, not to mention crippling economic depression, just as there was a more active Communist party at that time. In other words, our populations were exploring alternatives to the failures of the systems they had lived under, it is just that the failures of the Weimar Republic were more immediate and pronounced.
Another aspect is the greater freedom of speech and protest in the U.S. as compared to other countries; citizens in the U.S. are allowed (at the moment) to express their discontent with government policies, and public opinion sways leadership to a certain extent, probably mitigating the harsher excesses of big government. However, in the Weimar Republic, people were more "oppressed," in the sense that their voiced opinion had little effect on public policy; they required direct militia force to affect leadership.
We need to look at the experience of Germany in the recent World War to understand why it was so prone to take over by a totalitarian regime. It was battered and humiliated, and German national pride was very low. Therefore a totalitarian regime that managed to instill confidence once more into Germany was actually very popular.
The Weimar Republic was incredibly weak because of Germany's loss of WWI and also because of the hyper-inflation that hit Germany in the 1920s. There was also no long, strong condition of republican government in Germany as there was, by the 1920s, in the U. S., Britain, and France. In other words, the Weimar Republic was a fairly unusual case, especially when compared to the other three powers just mentioned.
The United States has its very foundation in democracy, and while there will always be contention between the two or more political parties, the country certainly wasn't in a fragile enough state to be taken over by a small, radical group. I agree with post #3 in that the tradition of democracy was fragile, and with a smaller, more desperate population, a radical group like the Nazi Party could seize the political imagination of the people and take over.
The United States did experience major social unrest during the post-war era, especially during the early years of the Depression. In many places, this came closer than we might imagine to revolution. This was true also of France and Britain. France, in particular, veered from far right to far left in the 1930s. I agree with post 3, however, that the desperate conditions in Germany, as well as an extreme sense of bitterness in the wake of World War I, paved the way for a radical response in Germany. Still, though, it didn't have to happen. Historians have emphasized a great deal of contingency in Hitler's rise to power, especially early on.
The previous post shows little understanding of history as the Weimar Republic was not taken over by an outside force. Therefore, isolation and militias (there were no "private militias" in the US at the time) had nothing to do with this.
These countries were able to avoid takeover for two reasons. First, they had longer traditions of democracy than Germany did. Germany had never really been a true democracy until after WWI. The other countries had. Second, Germany was much more traumatized by WWI than the other countries and was therefore more desperate for any government (even a totalitarian one) that would get them out of their troubles.
The United States has a very strong position because it is not next to many countries. Any country that wants to invade it would have to cross an ocean. The country is also quite large. If you are talking about takeover from within, the US constitution has a system of checks and balances and private militia to prevent that.