The war would have been longer, but the outcome the same. When France fell in mid-1940, Germany, Italy, and Japan fought Britain alone for a year without winning.
D-Day’s importance is a myth; we already had a “foothold in Europe” a year before (Italy), and D-Day was just to reduce the losses there. As another FReeper pointed out, Rome fell before D-Day.
What was the plan to get over the Alps into France and Germany.
The Germans had 100 divisions fighting the Soviet Union. Had they not been at war with the Soviets, How many of those divisions would have been deployed to the Italian theater. What would the Italian campaign looked like if a large portion of Army Group Center was in Italy instead of Central Russia.
Rome fell 4 June 1944. D-Day was June 6th.