If I recall from reading Joseph Balkoski's Omaha Beach, the weather was still a bit lousy prior to the landing. So this delayed the USAAF bombers, who then dropped their payloads further inland than would be useful so as to avoid hitting the landing troops. The bombing was to go until right before the landings so they erred on the side of caution.

Naval barrages were used prior to the landing craft shoving off from the mother ships, but again if you carried them on too long you run the risk of bombing your own land forces. The naval bombardment also did not last very long.

Balkoski's books though on D-Day really go into detail about the American landings and have excellent maps and figures to help understand the complexities of the landings and the improvising and adaptation of plans for things not going to plan (i.e. the lack of aerial bombardment and shortened naval bombardment).