It was. There were successful and fairly easy landings further west, but that still left a major bottleneck of the Cherbourg peninsula to fight out of. With Omaha and Dog beaches, the defenses were thickest. Air cover was not very capable, and much of the shelling had landed long - I understand it was expected that there would be tanks and artillery stored in the target zones. The biggest factors in the German defensive failure was the decoy operation with Patton's nonexistent army drawing their attention and planning further northeast. The second biggest was once the main thrust became clear to the local commanders, the "command-inertia" from Germany took far too long to bring up reserves.
As it was, it was close indeed - had the Germans been able to repulse successfully at the American beaches in the east, and had there been enough reserve support units, they could have moved up and driven the western beach-head into the sea. Too many of their forces were focused on the Dover-Calais route, and they didn't have the ability to shift that force by over 300km required to reach Caen and begin closing the door. A lot more could have been done with the naval gunfire to drop closer to the beaches, prior to the assault, but that would have also made the beaches that much more difficult to traverse - the same problems the infantry faced crossing the artillery's destruction in the first World War.
