Although Kennedy finally obtained a test ban treaty, the competition with the Soviet Union was far from over. The Soviets had successfully launched the first orbit around Earth in 1961, and Kennedy was intent on having the United States do the same. In 1962, he proudly congratulated John Glenn after Glenn became the first American to orbit the earth. Nevertheless, Glenn's accomplishment came after the Soviet Union's achievement. Kennedy set his sights on something bigger; he wanted to be the first country to send a man to the moon. The Apollo project would cost $40 billion, but Kennedy believed it was well worth it.

Not everyone agreed with Kennedy. NASA's Jim Webb put less importance on landing a man on the moon and more emphasis on gaining an understanding of space. Other critics argued that the large Apollo budget should go toward medical advancements and the revitalization of cities. Even Eisenhower gave his opinion. He believed that instead of focusing on placing a man on the moon, the space program should further the goal of military advancements. Not even talk of discontinuance of the Soviet moon project could persuade Kennedy to forgo his objective. If anything, polls throughout the world reflected the belief that the Soviets were more advanced, and this made Kennedy even more determined to surpass Soviet advancements in space.