"while they waited for the arrival of the Americans who were bound to find a way"

US Troops in England, 1944
Public DomainUS Troops in England, 1944 - Credit: UK Government
Perhaps the reason for this "widespread" faith in an American rescue was the USA's recent critical intervention in World War Two.

The USA had already overtaken Britain as the world's leading superpower, enjoying apparently boundless resources, military capacity and wealth.