It was the US that Brock the back of the Nazi blitzkrieg and forced Germany to pull enough units away from the eastern front to allow Russia to make a come back. In other words Russia only got to deliver the death blow because German was too busy fighting the western allies.
The Germans could have easily smashed any Anglo-American landings in Italy, had they not lost millions of men at Moscow, Stalingrad and Kursk. In July 1943, 63% of the German Army was in the East, and even in June of 1944, with Allied troops in Normandy and Italy, 62% of the German Army was still engaged against the Red Army in the East. Overall, for the entire war, 80% of German losses were sustained in the East. While Lend-Lease did admittedly help the Soviet troops, it was ultimately Soviet troops which broke the back of the Third Reich.
And if you're wondering where I'm getting these figures from, look up David Glantz's "The Soviet-German War 1941-1945: Myths and Realities: A Survey Essay."
Even before the US officially entered the war, the Soviets were still receiving aid via Lend-Lease. Furthermore, from September of 1942 to November 1943, during which US combat forces had just entered the fighting in the European theater, the Germans were still suffering 90% of their losses in the east. From November 1943 to June 1944, during which time US troops were fighting in Italy, 80% of German losses were still in the East. So it was the Soviets that did succeed in wearing down the German army. In fact, in June 1944, the manpower situation for the Wehrmacht had gotten so bad, aside from Omaha Beach, the units defending the Normandy beaches had entire battalions consisting of ex-Soviet POWs that had been pressed into service.
Again, these statistics are from David Glantz's above essay. The part about the Soviet POWs, though, I got from the below article written by English historian Anthony Beevor.