George Hicks reports on the invasion as set out by Radio Days:
The New York World Telegram called it "the greatest recording yet to come out of the war." This was the amazing recording made by George Hicks, London Bureau Chief for the Blue Network (soon to become ABC) of the beginning of the D-Day Normandy Invasion. To add to the amazement, until 1944 recordings of any kind on the air had been banned by the networks with few exceptions. The reason given was that they were a deception upon the public. But the New York Times concluded that "[transcriptions] can be more alive than a live program."
Update: What the people in the U.S. first heard about the invasion - from NBC: