FYI, they went in at low tide so the incoming tides would lift boats off as the day went on. The distance from the low tide line to the cliffs on Omaha was actually pretty far - here's a selection of images taken from the boats... ->

That's not to say you couldn't be hit, but having visited the beaches quite a few years ago, it's farther to the water than Saving Private Ryan made it out to be. This could have been a foreshortening effect caused by the camera settings and so on, but as someone else pointed out, it was something like five football fields in length from the bunkers to the boats when the invasion started...

You need to look into previous invasions of the allies, Torch, Sicily, Salerno, Anzio. Some met heavy resistance, others met light, so they pretty much knew they would meet some kind of resistance and some form of obstacles and fixed positions. What the infantry were expecting was that the bombers were supposed to provide the craters necessary for cover and to tear up the mine fields when they landed to avoid being exposed on the beach. Happened at Utah, not at Omaha. Most German WN points had defilade positions that shot perpendicular down the beach creating larger and deadlier fields of fire. Given most fixed positions that had case mates had their aperture restricted. So the weapon system can only face and traverse a certain direction.