No, the Soviet leaders weren't afraid that the US would attack, because they knew that US would never attack first. They also knew that if they attacked the US, the retaliation would be swift and terrible. That did not prevent them from using the US as a kind of a bogeyman to excuse the lack of consumer goods.
In the 1970s they were more afraid of the war with China, because they knew that if it started out as a conventional war, the Soviets would quickly get overwhelmed by sheer numbers, and would have to resort to nuclear weapons to keep from loosing.
