Like many, I always assumed that Hitler's knowledge and understanding of America was crude at best. This judgment is primarily due to the (infrequent) comments the Führer made about the United States in his speeches. But one needs to separate Hitler's propaganda from what he actually thought. As the professor of history Klaus Fischer documents in his 2011 book Hitler & America, the Führer in reality had a nuanced understanding of America. Hitler was not an educated man, and, unlike Roosevelt, who as a boy would summer at Bad Nauheim and had first-hand knowledge of Germany, Hitler never visited America, nor did he know many Americans. But Hitler was an autodidact and was very curious about America. Furthermore, he listened to some his advisors - such as Colin Ross or Ernst (Putzi) Hanfstaengl - who had a deep knowledge of the country. (Hanfstaengl's mother was American; he later switched sides and advised Roosevelt on the Germans).
As a young boy, and like many German and Austrian children of that era, Hitler was fascinated by the western novels of Karl May. They captured his imagination and molded his opinion of America, while also influencing later his drive to procure Lebensraum for the German Volk. The vast steppes of Russia were his wild west, and the Russian people his Indianer - an inferior race that must be enslaved or exterminated.
Fischer's central thesis in the book is that Hitler had a split image of America - which he calls America/Amerika. On the one hand, Hitler admired America's industrial power, which he attributed in large measure to the influx of millions of German immigrants. Germany's sacrifice of blood to the New World should have brought both nations together in a sacred alliance. On the other hand - the darker Amerika side of the equation - Hitler felt that America's lack of ethnic cohesion - the mixing of disparate races - had transformed the country into a "mongrel nation". America was culturally hollow, the glittering facade of Hollywood masking a vast Potemkin village. Hitler concluded, therefore, that America would never have an effective military, since the galvanizing idealism of Nazism was lacking in the soulless nation.
As Fischer shows in the book, Hitler had a shrewd understanding of American politics. He saw that the Republican Party was isolationist, and, in many ways, sympathetic to his goals. The Führer nurtured Germany's ties to the America First crowd - led by the Nazi sympathizer Charles Lindbergh. He hosted a meeting with Herbert Hoover in Berlin. Hoover, an engineer by training, marveled at the Nazi's massive infrastrucure projects. Hitler's goal all along was to keep America neutral for as long as possible - until at least he had finished his project on the European continent. This strategy was largely successful until Kristallnacht in November 1938.
President Roosevelt posed the greatest threat to Hitler's strategy of keeping America neutral. Hitler recognized early on that his nemesis was an interventionist; he suspected that Roosevelt might be Jewish, but, at any rate, was a puppet for Jewish interests. Hitler did what he could to forestall Roosevelt, including financially backing the labor leader John L. Lewis in the 1940 Democratic Convention.
With respect to Hitler and Roosevelt, there remains a puzzling question: why did Germany declare war on the United States on December 11, 1942? This has never been answered satisfactorily, but Professor Fischer theorizes that Hitler felt that the "unnatural alliance" between the United States and the Soviet Union could not be sustained. Here Hitler may have been correct in his assessment but he got the timing wrong; the alliance came apart only after Germany was destroyed. Secondly, Fischer hypothesizes that by December 1942 Hitler realized the war against the Allies could not be won, but the war against the Jews was certainly winnable. He had been holding the Jews in Europe hostage to keep America out of the war. By declaring war on the United States, Hitler could commence with the "Final Solution", and Fischer believes he gave the order within days of December 11. In any case, Fischer's theory is fascinating.
In the end, as the Red Army was closing in on him in Berlin, Hitler made a surprising statement while dictating his political testament (Bormann Vermerke):
"This war against America is a tragedy. It is illogical and devoid of any foundation of realtiy."
Hitler believed his own propaganda, that America had been dragged into war by FDR and the Jews. He and the Goebbel's propaganda machine warned the German Volk that the Americans were just as bad as their Bolshevik counterparts; both were controlled by bloodthirsty Jews who would enslave the German people. But the "Volk", it turned out, did not believe a word: once the war ended Germans did everything they possibly could to flee to the American Zone.