The short answer to the question "what convinced many Americans that the United States needed to prepare to enter World War II?" is "nothing."
Most Americans were opposed to getting involved in another European war. President Franklin Roosevelt, who believed firmly that another major conflict was developing in Europe, especially given Adolf Hitler's threatening rhetoric and demonstrable moves to rearm Germany, maneuvered carefully to prepare the United States for what he believed was inevitable. The United States, however, despite some levels of industrial mobilization, mainly to support the British and, later, the Russians, was woefully unprepared for the war. It was not until the Japanese attack on U.S. military forces in Hawaii and the Philippines in December 1941 that the American public became outraged and committed to the defeat of the Axis. The United States Army was completely unprepared, and it was only fortuitous that the Navy's aircraft carriers were on patrol at the time of the attack on Pearl Harbor. Had the carriers suffered the same fate as the battleships, the war against Japan may have gone very differently.