The Russians had been pushing for a second front for a long time, but there was always some excuse not to . By Mid 1944, it had really become a non-issue. I realize that you will never find this assessment in any US or British publication. The line here is that the Nazi war machine was destroyed as a result of the landing in Normandy. A true absurdity to anyone remotely knowledgeable about the events on the Eastern front during 1943 and early 1944.
There is no doubt that US and British bombing of German industry had greatly hurt the Nazis, but the bulk of the German army, millions of men and hundreds of divisions, had been destroyed on the eastern front. It is not for nothing that Colonel Klink of Hogan’s Heros fame was so horrified by the threat of being sent to the Russian Front. It was essentially a death sentence.
In the year and a half or so after the battle of Stalingrad, the Nazis were pushed all the way back to the Warsaw area in heavy fighting. There was a D-Day scale battle at least every week. At Kursk in July, 1943, something like 1500 German tanks were destroyed. After that the retreat became a bit of a rout.
It is not far from Warsaw to Berlin. With or without US and British ground troops, it was clear that the Russians would soon be in Berlin and the US and Britian would not be there to save German capital.
It is even concievable, though not certain, that the Russian advance would have continued to Spain to overthrow the fascist Franco regime there.
I guess it is possible that the Germans were fooled by the Calais ruse, but I think it is a stretch. How it could work is beyond me.