Ok, to your main point. The USA believed it needed combat experienced divisions for D-Day, and that can only be done fighting. Carl is correct that we wills still go to Sicily. We like to do invasions with land based air cover. And with a lot more German/Italian divisions, there is no really "soft" place to land. Even if the USA goes for the Balkans, then the Germans will quickly reinforce and stall the front. So mostly likely, it is Italy or bust.
If Sicily fails, then the senior officers involved will be sideline to support roles as happened with other officers IOTL. Or perhaps retired. Imagine something such as Patton as US General in charge of logistical operations in North Africa. And Bradley being the equivalent of a TRADOC officer in the USA. My best guess is that Italy stays in the war til the end. After defeating the USA invasion in 1943, the next one will be in France in 1944. And Mussolini will have defeated the USA where Germany failed. So Mussolini makes it to the very end of the war.
As to Stalin, it will greatly reduce his respect for the USA military ability. It will also be another in a list of British defeats (France 1940, Malaysia 1941, Sicily 1943, Burma). It really feeds into the democracy has weak armies idea. We are corrupt, weak people. Now I know you want to skip the Eastern front effect, but there is some fascinating interplay if the Soviets do much worse than OTL (Kursk works?) and the USA is viewed as an ineffective ally. But then we get into the really complex environment of the Germans having more resources in the east and months to plan their use. And if the operation in Italy fails, won't the Germans pull most of their troops from Italy once the Americans are driven into the sea, and it is clear that we are now diverting shipping to England.
BTW, with Sicily in Italian hands, doesn't that mean that Allied shipping stays out of the Med. This would make logistics much harder since ship have to go around Africa.
I don't think we can accelerate the D-Day operation by much. What month did you have the failed Sicily landing happening? And what changed to allow the destruction of the Luftwaffe in Feb/Mar 1944. We destroyed more German planes in two months than all previous months combined. So we roll into 1944. D-Day should still work. All those German units beat in Italy will have to be broken in France or Russia.