If Hitler had managed to take Britain then the U.S. government would have done nothing. Sorry to say but the fact was that most of the government was pro Nazi Germnay and not willing to enter the war. It was Roosevelt who was one of the few that would have backed Britain. I also have no doubt that with Britain beaten Hilter would have focused more on the bomb and would have won the race to building it and with the V9 rocket would have been unstopable.
The real threat for the US was in Russia, if the Nazis had taken that they would have had a base to attack North America.