I know that publicly there was never any acknowledgement that defeat was a possibility except in the context of exhortations to fight/work harder, but AFAIK Churchill at least was convinced for most of the Battle of Britain that Germany was about to invade and Britain would be overrun, and I imagine that the unbroken string of defeats in the early stages of the Pacific War and the poor performance of the Americans in their first battles in North Africa didn't do much for Allied confidence either. I also know, though, that the Allies were often wildly overconfident, for example about the effectiveness of aerial bombing at crippling German production. Given that, was there already a unanimous belief that an eventual victory was inevitable before Stalingrad? Or, on the other hand, did anyone in the know continue to fear defeat into late 1943 or even 1944, or take setbacks like the debacle at Anzio as evidence that Germany was turning the war around?
From Churchill's own memoir, immediately after Pearl Harbor. Apologies for the long quote:
No American will think it wrong of me if I proclaim that to have the United States at our side was to me the greatest joy. I could not fortell the course of events. I do not pretend to have measured accurately the martial might of Japan, but now at this very moment I knew the United States was in the war, up to the nec k and in to the death. So we had won after all! Yes, after Dunkirk; after the fall of France; after the horrible episode of Oran; after the threat of invasion, when, apart from the Air and the Navy, we were an almost unarmed people; after the deadly struggle of the U-boat war - the first Battle of the Atlantic, gained by a hand's-breadth; after seventeen months of lonely fighting and nineteen months of my responsibility in dire stress. We had won the war. England would live; Britain would live; the Commonwealth of Nations and the Empire would live. How long the war would last or in what fashion it would end no man can tell, nor did I at this moment care. Once again in our long Island history we should emerge, however mauled or mutilated, safe and victorious. We should not be wiped out. Our history would not come to an end. We might not even have to die as individuals. Hitler's fate was sealed. Mussolini's fate was sealed. As for the Japanese, they would be ground to powder. All the rest was merely the proper application of overwhelming force. The British Empire, the Soviet Union, and now the United States, bound together with every scrap of their life and strength, were, according to my lights, twice or even thrice the force of their antagonists. No doubt it would take a long time. I expected terrible forfeits in the East; but all this would be merely a passing phase. United we could subdue everybody else in the world. Many disasters, immeasurable cost and tribulation lay ahead, but there was no more doubt about the end.
Of course this was written after the war, but the text of the printed telegrams generally echo the same sentiments; even in the immediate aftermath of the debacles of the fall of Singapore or the surrender of Tobruk, there's never a sense that he felt that the war wasn't going to end in an Allied victory of some type.
It's fair to say that there were some topics on which Churchill's memoir isn't an honest reflection of history, especially ones which touch on US/UK divergences. But he had good reason to believe that, the moment that the US became officially involved in the war, ultimate victory was sealed. The US had vast manufacturing power and huge reserves of manpower, and was in an unassailable geographic position, and it was only a matter of shipping limitations that caused things to take as long as they ultimately took.