I've always held the belief that any dreams Hitler had of occupying the UK were dashed in the 'Spitfire Summer' of 1940. The allies had a tenuous air superiority from then on that only grew until it was completely dominant (chalk it up to bravery, ability, and poor decision making by the German high command). I don't for a second think that the UK could ever be taken.
My opinion of Germany's best case scenario would be an occupation of the continent, from western France to their own eastern borders, with parts of Poland as a weakly held buffer. Eventually partisan efforts and Russian/allied (even without the US) pressure would lead to collapse, if it hadn't internally already (remember, Hitler wasn't universally popular even in Nazi Germany).
All that said, I don't think the United States really had a choice in the matter. The UK was an ally, and though it took Pearl Harbor to actually get an official declaration, Roosevelt was already doing what he could to help the British cause, mainly in the form of war materials.
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