When do you suppose was the last time an American citizen felt the need to seek political asylum in a foreign country? Daniel Ellsberg didn't do so. Maybe a few draft-dodgers during the Vietnam War? Prior to that I just don't know.
And...through the power of Google, we have some answers:
Bobby Fischer went to Iceland.
Benedict Arnold went to London.
Twenty-one American POWs defected to China during the Korean War.
Aside from the above listed "Benedict Arnolds" (and how'd you like to know your name has gone down in history as a traitorous asshole?), I couldn't find any other examples of American citizen choosing to leave the country out of political necessity.