I've seen movies where a bunch of battered British citizens and soldiers sit around a radio waiting for news. In the movie, when the announcer says the United States has joined the war effort they cheer and look relieved. How accurate is that? Did we really make that much of a difference? Or is it just false drama thrown in by movie directors?
Churchill famously said on December 7th 1941 (just after Pearl Harbor): 'Consider the tide turned. The accession of the United States makes amends for all, and with time and patience will give certain victory.'
Evidently some of the European Allied forces understood the momentum and impact the US would bring to the War, however it is certainly questionable if the average British Tommy comprehended this. Admittedly another ally was not a bad thing, and especially the US at that, however it was not until the Italy landings in mid-1943 and DDay in 1944 that the US forces made a significant impact on the European theater. Churchill knew it would take time but in contrast the British population might have expected something sooner and been more enthusiastic earlier on... However, in all likelihood they were probably more busy worrying about the next shipment of tea, air-raids and European conflict to worry too much about the Americans and what they were up to and who usually they traditionally treated with indifference or suspicion.
Also as you mention, there is always room in movies for dramatic licence!