The invasion began at daybreak and it wasn't until almost noon when the German resistance at Omaha fell apart. If I remember right, there was sporadic sniper fire on the beaches for the rest of the day, but all afternoon the Allies were able to bring troops and equipment into France at will.

My wife's grandpa went ashore on something like D+4 and said the beaches were like Grand Central Station by then. He had no concept of what had happened juts a few days earlier until after the war.