To follow up:
How would the Allied and Axis powers responded to such a failure?
Where there any crucial events that had to happen to ensure success?
I know this doesn't answer the question directly, but it is a good point on how difficult the landings could get and the potential for them to fail.
"At one point, General Omar Bradley was so distressed that he considered withdrawing the Omaha landers, and instead moving his forces to Utah Beach. US Navy destroyer McCook's captain Lieutenant Commander Ralph Ramey, seeing the dangerous situation, ordered his ship against battle plans to sail closer to shore and bombard enemy defenses. As other destroyers followed suit, the naval fire was able to alleviate the pressure for landing troops. The destroyers' 5-inch guns destroyed several German gun emplacements and allowed the landing troops to advance." - C. Peter Chen, 'Normandy Campaign, Phase 1'