If we hadn't won at D-Day we would have given a boost to German morale. But the Soviets would have soldiered on.
By 1944 Germany had lost. The Soviets had built up a huge amount of momentum and the German army was incapable of stopping them. United States troops would have continued to advance up through Italy, and Churchill would probably have got the invasion of Yugoslavia he was hoping for.
In all likelyhood the Soviets would have taken Moscow before the first atomic bomb was ready. And even if they hadn't Germany would have been so battered that it's reasonable to believe that the first atomic bomb would have been used om Japan anyway.
The fate of the invasion force also depends on what you mean by the landings failed. Do you mean that the fighting lasted into June 7th before stopping? Or that the allies were forced out of France after a month of fighting. The latter, while far more damaging to the Allies, is far less likely then the beach landings simply being defeated. If the beach landings had failed then there would have far more then 3,000 casaulties. But despite the loss of the entire airborne invasion force, the Allies still would have had a huge stockpile of supplies in Europe.
There would have been another landing, but if that landing came too late then there is the very real possibility that France, or parts of it, would have been liberated by the Soviets. With the result of an entirely Soviet Germany, and France becoming either a split or communist state.