Point of order: In retrospect we can clearly see that the RAF was losing the Battle of Britain. It was within weeks of being completely eliminated by the Luftwaffe, when Hitler, quite unexpectedly for the British, switched to a strategic bombing campaign of major population and industrial centres. If the Luftwaffe had air supremacy, then naval supremacy and invasion would have followed. Invasion would have left very few credible options for any D-Day like operations.
The United states was already giving overt aid to Britain at that point. Had RAF lost and the German invasion of Britain seemed realistic, the USAF would have joined in to prevent that. While it would have taken only weeks to end the RAF, Germany didn't have the shipping capacity to maintain an invasion, and it would have taken months to build.
Also, few considered air power to be actually capable of fighting battleships until the Battle of Taranto, where the effectiveness of air raids surprised almost everyone. The German planners almost certainly didn't believe in the capability of Luftwaffe to destroy the Royal Navy.
The US Navy was actively fighting the Kriegsmarine on the North Atlantic as early as late 1940, and even before that, US had started providing armaments to bolster the British war effort, and took over the defense of various British holdings to free up forces. They also provided entire cohesive units of equipped volunteers to fight against the Germans on the British Isles, and the Japanese in China. None of these actions were neutral under international law -- the United States was in a state of undeclared war against the axis powers for nearly two years before Pearl Harbor. This all can be found in any reasonably comprehensive history of the second world war, including the wikipedia articles on the Atlantic War and the Sino-Japanese war.
The reason USA didn't join outright was that there was serious domestic opposition to the war, and Roosevelt understood well that he needed his Lusitania to be able to bring America fully into the war. The Germans took all pains to avoid this, and USA only managed to declare war after the Pearl Harbor.
In reality, history rarely contains black-and-white narratives where the one side is the clear aggressor. Had the USA not been actively engaging in combat operations against the Germans and the Japanese, they never would have been stupid enough to pick a fight with the Americans.
Exactly. From where could the USAF operated? I agree that the Americans would liked to have helped resist an invasion but at that time I don't think they would have had the required platform.