the verb "mögen" (mag) requires an accusative object. Since it is accusative case we just have to look up http://www.canoo.net/inflection/schweizer:N:M and see that "den Schweizer" is singular noun in acc case meaning "the Swiss (person)".
"The public likes the Swiss (plural)" would be "Das Publikum mag die Schweizer."
Since I am not a native English speaker that which you've written confused me: ".... a certain person that comes from Swiss". Can we really substitute "Switzerland" with "Swiss" ?
Using "likes" after a singular collective noun is American English, whereas using just "like" after a singular collective noun is British English. I have, however, never seen German use any verb ending with "-en" after a singular collective noun, so I presume that there is only one correct answer in German.