What if Nazi Operation Sea Lion goes ahead, and is a miserable failure

While many people popularly criticize Hitler for failing to proceed with an invasion of Britain in 1940 or 1941, personally, I think the strategy he adopted was the only realistic one possible. After all, he had virtually no surface fleet. Even given temporary air superiority over the English Channel, which he might possibly have achieved, his forces would have faced the entire British Navy in speedboats. Presumably, they would have been exterminated, almost to a man. True, the British Navy would have suffered substantial losses from air attack, but it wasn't really that easy to sink a battleship in open water with the bombers and attack aircraft of the day. So, rather than lose a million men or so, for absolutely nothing, Hitler resigned himself to a strategy of bluff and intimidation, which Winston Churchill was more than capable of dealing with. So, let's suppose Hitler is enough of a fool to try it anyway. He loses a hundred divisions or so in a few hours of fighting, a disaster far worse than the Battle of Stalingrad in its entirety. What happens next? He can probably still hang onto France, he's still allied with the Soviet Union, and the French are totally prostrate. But, Stalin won't be impressed with his total failure, will he now? Stalin may start pressuring Hitler in ways that will make the German leader uncomfortable. Worse still, Stalin's likely to warm up a bit to Britain too, being the practical man that he is. And what can Hitler really do about it? He probably won't have the support or the military strength to mount an invasion of Russia, even if he wants to. An American entry into the War seems less likely, because the Japanese are likely to view Hitler's failure with some alarm, and think twice about a strategy of invading Singapore, Hong Kong, the Philippines and the Dutch East Indies. The British are likely to have additional forces available to defend their territories, given the Nazi debacle in the Channel. Thus, probably no Pearl Harbor attack, no forced American entry into the War. Will Hitler offer Peace terms with Britain, including partial withdrawal from France? This would seem reasonable, but rather out of character for Hitler.