I'd argue that by June 1944, Germany had already lost the war, and it was really just a matter of time before Germany either surrendered or got ran over. The Germans were on the retreat for almost a full year prior to D-Day, and their strategy was entirely defensive. Their last major offensive in the east was in July 1943 (the Battle of Kursk) which ended quite badly for them. After that point, the Germans limited themselves to merely trying to slow the Russian advance, again without much success. It was becoming clear that sooner or later, the Russians would be in Berlin. That means the D-Day landings weren't really crucial to defeating Germany. They certainly hastened the end of the war. However to say by how much is difficult - the bulk of the German forces still remained in the east even after the allies had landed.

Now, I need to make clear that while the D-Days landing and the opening of the second front weren't crucial to defeating Germany, that is NOT to say that the allies had a small to the overall defeat of the Nazis. Other theaters, such as the Mediterranean, the Atlantic, the skies over Germany were all quite important. Secondly, it is hard to understate the value of allied aid to the Soviet Union in the form of raw materials, weapons, machinery, food etc. All those things combined were all quite essential to victory, and had probably as much if not more impact as the Soviet drive from the east. In fact, the Soviet offensive probably would not have been possible otherwise.

http://deanoworldtravels.files.wordpress.com/2012/07/allied_invasion_force.jpg http://upload.wikimedia.org/wikipedia/commons/4/44/BagrationMap2.jpg

Just compare the forces and how few troops were spared for the west. D-day was an moderate annoyance compared to bagration