Quite the complicated situation. At the time Churchill took power he was leading the country to fight against long odds. It was only Hitler’s Operation Barbarossa - the invasion of Russia - which diluted the threat of immediate invasion of Britain. The defeat of the Luftwaffe in the Battle of Britain was a close-run thing, and would not have happened without the diversion of the German attacks from the RAF to the British civil population. And that might not have happened but for the RAF’s attacks on German civilians, which followed putatively accidental bombing of British civilians. Both the British, who failed to pick the right horse when they didn’t significantly back the RAF’s Frank Whittle in his jet engine work, and Hitler when he didn’t allow the Me 262 to be developed as a fighter but insisted on a bomber version - blundered in ways that could have completely changed the air war.Churchill claimed that he didn’t want American troops but only American materiel in order to defeat the Nazis, was not honest about the actual situation.
Meanwhile FDR was more interested in the fate of the USSR than anything else. He began harassing German U-boats in international waters after the start of Barbarossa.
But FDR committed the US to production mobilization immediately upon the Fall of France in mid-1940. That was when Churchill sent all Britain’s military technology to the US, including the blueprints for the Merlin aircraft engine, radar, Frank Whittle’s turbine, and other things.
Wow I am learning all kinds of stuff.