All this happened because the German air force was a spent force. Its best pilots were dead, its propeller-driven fighters increasingly obsolescent and short of fuel, and its fighter strength worn down attempting to stop the American strategic bombers and their Mustang and Thunderbolt escorts.
But Germany had a "wonder weapon." The Me-262 jet fighter flew 150 miles faster than propeller-driven Mustangs and Spitfires. It didn't effectively enter the war until late 1944, a victim of teething troubles and Hitler's insistence in 1943 that it should be built as a jet bomber.
But what if Hitler hadn't meddled, or a crash development program had enabled jet fighters to fly in significant numbers on D-Day? The Luftwaffe's bomber fleet was a skeleton force by the summer of 1944, so the invasion probably wouldn't have been disrupted by bombing. But large numbers of Me-262s might have driven Allied bombers from the sky, enabling the panzer divisions to operate in daylight with impunity.
Poison gas. One of the most intriguing mysteries of World War II is why Germany and the Allies did not use chemical and biological weapons against each other. As the Third Reich crumbled, it seemed ever more likely that Hitler would employ weapons of mass destruction.
The reason he didn't was deterrence. Both sides feared that, as in World War I, once one side used chemical weapons, so would their opponents. It turned out that German nerve gases like sarin were far more effective than Allied chemical weapons, such as mustard gas, but the Germans didn't know that.
Allied retaliation would have come swiftly (Britain and America had produced large quantities of anthrax bombs to drop on Germany), but the immediate question is the impact of nerve gas on an amphibious landing. Landing on a fortified beach was difficult enough. Doing this while wearing a gas mask would have been a nightmare.
Finally, it is important to remember that even if D-Day had failed, the war would have continued. Despite Hitler's hopes that defeating D-Day would persuade the Allies to seek peace, the Soviet armies would have continued to march on Germany, and the Allies would have eventually mounted another invasion. The war would go on until the Third Reich was gone.