As stated by American Luke - saying that there was no preliminary bombardment of Omaha Beach is incorrect.
Immediately before the landings were due to start the beach defenses were subjected to a 40 minute naval bombardment and a 30 minute aerial bombardment.
The Naval Element of this bombardment was to be provided by:
USS Texas (Battleship), USS Arkansas (Battleship), HMS Glasgow (Light
Cruiser), HMS Bellona (Light Cruiser), Montcalm (French Light
Cruiser), Georges Leygues (French Light Cruiser), USS Frankford
(Destroyer), USS McCook (Destroyer), USS Carmick (Destroyer), USS
Doyle (Destroyer), USS Emmons (Destroyer), USS Baldwin (Destroyer),
USS Harding (Destroyer), USS Satterlee (Destroyer), USS Thompson
(Destroyer), HMS Tanatside (Destroyer), HMS Talybont (Destroyer), HMS
-"Omaha Beach: D-Day, June 6, 1944" by Joseph Balkoski, Pages 79 - 80.
However, this bombardment was, and is, considered insufficient.
In general, it is believed that the time available for pre-landing bombardment was not sufficient. German defensive positions were well camouflaged and strong. It is considered that these positions should be destroyed by slow aimed fire from close range, prior to the landing. Something more that temporary neutralization is required when troops face beach mines, wire, anti-tank ditches and similar obstacles after landing.
-Rear Admiral John Hall, Force O, Operation Neptune Action Report, July 1944.
According to various sources (including the Wikipedia Article on Omaha Beach) 2 Battleships, 3 Cruisers and 12 Destroyers were tasked to Omaha beach. One of the battleships involved was USS Texas (The other was the USS Arkansas) fired 244 14" Shells in the first 34 minutes of D-Day, which equates to 7.5 Shells per minute (Source). Assuming at the USS Arkansas achieved a similar rate of fire, in excess of 450 14" shells were fired in this time frame.
On it's own this is an incredible amount of fire and when you factor in the secondary batteries of both Battleships as well as the gunfire from the Cruisers and Destroyers the preliminary bombardment of Omaha Beach cannot be considered insubstantial.
The aerial element of the preliminary bombardment was tasked to the 2nd Bombardment Division of the US Eighth Air Force. ("Omaha Beach: D-Day, June 6, 1944" by Joseph Balkoski, Page 76) which was made up of some 400 B24 Liberator Bombers.
A B24-J could carry a maximum of 8,800 lbs of bombs on a short range mission. This means that the 400 B24s assigned to Omaha Beach could drop a maximum of 3,520,000 lbs of bombs on Omaha Beach.
However, due to the fact that the nature of bombing in Europe (in that it was inaccurate due to the altitude it was conducted from) the bomber force was limited to using 100 lbs bombs in order to prevent the beach from becoming heavily cratered and therefore impeding the effectiveness of the bombers against the bunkers defending Omaha Beach. ("Omaha Beach: D-Day, June 6, 1944" by Joseph Balkoski, Page 78)
While this bombardment was considered insufficient, it was not all that insubstantial. The bombardment described above represents the expenditure of a substantial amount of munitions in a confined area and time space.
The insufficiency of the bombardment can be seen when the preliminary bombardment of Omaha Beach is compared to the bombardments seen in the Pacific Theatre. For example, the Invasion of Noemfoor, in 1944, saw a preliminary bombardment that was carried out by 5 Cruisers and 25 Destroyers. (Source) Granted, there were no Battleships but there is a large difference in numbers.
While the bombardment of Noemfoor was considered to be highly effective, the same cannot be said of the 1943 battle of Tarawa Atoll. At Tarawa the Japanese were bombarded for 3 hours by the flotilla (that consisted of 17 aircraft carriers, 12 battleships, 8 heavy cruisers, 4 light cruisers and 66 destroyers, although I am unsure of how much of this Flotilla was involved in the bombardment). This bombardment failed to cause any major disruption to the Japanese defenses. This shows that even a preliminary bombardment that was nearly 5 times longer in duration and from a larger flotilla than at Omaha Beach failed to cause any major disruption to the defender.
When all of these factors are combined, along with other salient factors such as the time of the bombardment (~5.50am) which hampered the ability of Naval gunners to spot their targets due to low light, it is evident that the bombardment was never going to have the desired effect on the defenders of Omaha Beach.