Thanks to naval gunfire and good leadership, it got taken by the end of the day.
Naval gunfire was an overwhelming advantage in US amphib operations. With air superiority, nothing could really stand up to it for long, and by the Normandy landings, we were past air superiority and almost at air dominance. Look at what happened at Salerno, where even with elite mechanized forces (Which were not available to the German defensive zone commanders at Utah or Omaha) and superior forces the Axis could not crush the beachhead because nothing that came within sight of the bombardment ships could survive the pummeling that would immediately ensue.
The one amphib op that was a dismal failure was Dieppe, but it was a large scale raid which was never intended to create a permanent lodgment. It was also quite poorly-planned and executed, not well-resourced, and lacked the air superiority necessary to let bombardment ships close to point-blank range (If there had been a good bombardment plan with sufficient ships committed to it in the first place, that is).
