The big problem was the weather, they had already postponed one day due to storms. If they didn't go on the 6th they were stuck for a month until the tides were right again.
Plus once the paratroopers had dropped that was it, no choice but to go ahead with the seaborne landing unless you wanted to consign them all to death or captivity.
On the whole it didn't work out too badly. They Allies had already had a near disaster with a seaborne landing at Salerno https://en.wikipedia.org/wiki/Operation_Avalanche where the Germans nearly over-ran the beach-head. Far more desperate situation than Omaha, bad as that was. But that was in the Italian campaign so everyone forgets about it.
Current Lash Up:
TEAC VRDS 701T > Sony TAE1000ESD > Krell KSA50S > JM Labs Focal Electra 926.