John Cheever's short story "The Swimmer" was published in 1964. The setting of the story is the American suburbs, which flourished following the end of World War II. While no definitive date is given in the story, based on publication date and the themes and setting of the story, it would be safe to assume it takes place during the 1950s, or possibly the very early 1960s.
It seems as your question really is the purpose of the author. Cheever often wrote his stories without time reference in order to make it "universal". It is a question of allegory wether or not Neddy is undertaking his advandture within one day or one year or even a dacade.
If you consider the time frame "The Swimmer" was written in, you certainly have the 1960's and even the late 1950's, when suburbs grew and many Americans were frightened by the Cold War that could have led to an atomic war and thus destruction of all major cities of the US and most certainly the Soviet Union.