Until they were within a few hundred yards of the beach, no the troops landing at Omaha beach were generally expecting very limited resistance. They had been briefed that air force bombers, navy battleships and landing craft firing rockets would kill or stun the defenders.

There was a massive disconnect between the Omaha Beach bombardment plan concept and it's implementation. A full discussion is probably out of scope for this question but the troops were expecting to essentially mop up the few dazed survivors. However the bombers delayed their release for so long that all the bombs landed well inland. The period allotted for naval gunfire support was only around 30 minutes and the number of ships allocated was too few. Meanwhile the only noticeable effect of the highly inaccurate rockets was to start some brush fires on the bluffs.

The planes flew so high above the cloud cover that the assault troops never saw or heard them. The naval bombardment was very impressive as were the rockets and they did give the troops some hope for an easy landing. Once they were within 300-400m of the shore it became obvious that the defenses were barely scratched.

It's worth pointing out, though, that the experience of troops landing at Omaha varied widely depending where and at what time they landed. The troops landing on the Western part of the beach in the first wave were all but exterminated. First wave troops landing on the far Eastern edge covered by smoke from the fires made it to the sea wall almost casualty free, but often very far from their intended landing zone. Subsequent waves took significant casualties even before landing, from mined beach obstacles and from direct and indirect artillery fire.

Source : Omaha Beach, Joe Balkoski

Beyond the obvious fact that most of the soldiers knew they were attacking a well-fortified beachhead, many believed that really staunch resistance would be dealt with by the air and naval bombardment prior to landings. Anthony Beevor argues that many of the men in the first wave truly believed that the Navy and Army Air Corps had done a satisfactory job of softening up the defenses. As Beevor explains in his study, “The first wave of troops in their landing craft had been deeply impressed by the heavy guns of the battleships. Many compared the huge shells roaring over their heads to “freight cars”. At a given moment, the landing craft, which had been circling offshore to await H-Hour, then headed towards the beach. The absence of fire at that stage aroused hopes that the Navy and Air Force had done their work as planned.” As the boats moved in closer to the beach the “pinking noises” of bullets hitting the landing craft revealed that the beach defenders were firing on them, and showed them that the enemy was still very much alive. At that point it was pretty obvious that they were attacking an enemy who had been preparing for this moment for some time. However, as the pinking noises continued many officers tried to keep their men inspired to storm the beaches. One officer reportedly shouted to his men, “Make it look good men, this is the first time American troops have been here in twenty-five years!” So to directly answer your question, I do believe, that these men clearly believed there was a solid chance they would die. However, they simply could not tell what their fates were prior to getting in close enough to see what the Germans would throw at them.

Antony Beevor, D-day: The Battle for Normandy. (New York: Viking, 2009).