The major potential problem that the US had with the USSR was that the Soviets might take over too much of the world and leave the US isolated. We believed that the Soviets were hostile to us and our way of life. We therefore believed that we would be in trouble if they were to take control over too much of the world.
Right after WWII, it was clear that the Soviets were going to hold on to all of Eastern Europe. They had also grabbed North Korea and had pressured us to let them have part of Japan as well. This looked like they were an expansionist power. Therefore, we worried that they would try to take Western Europe and perhaps East Asia. If they accomplished these things (assuming they were hostile to us) we would be more or less alone and without allies in the world.