Gen. Bradley indeed did briefly consider pulling off of Omaha and transferring westward to Utah. The US forces were unaware of the presence of the German 352nd Infantry Division, which had artillery and Panzer components.
Here’s a map in nice detail that helps make things more clear about the scale and spacing:
http://upload.wikimedia.org/wikipedia/commons/8/8e/D-day_battle_order.jpg
What kept the US on Omaha was the brave actions of a couple of destroyer commanders, who pushed their destroyers very close to shore (much closer than orders allowed) and commenced to putting direct fire from their 5-inch guns onto the German bunkers and gun emplacements.
Stephen Ambrose in "Citizen Soldiers" said that they, including a Polish destroyer, came in so close, their hulls were scraping bottom. Their fire was directed by some guy on the shore with a WWI signal lamp - the guys sent ashore to do this were all killed and their equipment destroyed. Point blank range with those guns saved many lives.
