Even as the president plays down that possibility, the C.D.C. chief and other experts warn of a dual challenge. Could the United States face two epidemics at the same time next fall, flu and the coronavirus? That frightening idea was raised by Dr. Robert Redfield, the director of the Centers for Disease Control and Prevention, during an interview on Tuesday with The Washington Post. He suggested that a new surge in coronavirus cases could coincide with the next flu season, causing an even more difficult crisis than the one the nation is facing now. “We’re going to have the flu epidemic and the coronavirus epidemic at the same time,” he said. He added: “The key to my comments and the reason I really wanted to stress them was to appeal to the American public to embrace the flu vaccine with confidence. One of the greatest tools we have as we go through the fall-winter season is to get the American public to embrace the influenza vaccine and thereby minimize the impact of flu to be the other respiratory disease we confront.”