"City on a hill" is not a term that originated not with either President Reagan or Massachusetts' Puritan Governor Winthrop, but in the Sermon on the Mount, attributed to Jesus.
Winthrop did write a speech (not sure it was a sermon), but it was not about "this country." (Apart from native Americans, to whom Winthrop definitely was not speaking "this country" consisted at that point mostly of trees and rivers and was by no means even considered a "country.")
Winthrop wrote the piece either in England or on the ship that was bringing him and other Puritans to these shores for the first time in 1630 (i.e., not the original bunch of Puritans that landed in Plymouth in 1620). And he delivered it on the ship.
He was basically exhorting the members of his group to work together once they got here, so they would survive, not saying that "this country" is at its best when we all help each other, as Bashir says.
Reagan and Winthrop are not the only politicians who used the term, either.
John F. Kennedy used it in a speech to the Massachusetts General Court (the Massachusetts legislature)shortly before being inaugurated President of the U.S.
Whether Reagan and his people got the term originally from the Gospel of Matthew, from Governor Winthrop or from JFK, I have no idea. I would be surprised if Bashir knows.
Now, every politician seems to aspire to be as well loved as Reagan. When Reagan gave his city on a hill speech in 1974, though, I am guessing that every politician, including Reagan, aspired to be as well-loved and well-remembered as JFK was in 1974.
So, I would not be surprised if Reagan and/or his speechwriters had looked to JFK's speeches for "inspiration." Then again, Reagan was supposedly very influenced by the church he had attended as a boy. I would put Winthrop's sermon third in likelihood as having been Reagan's first thought. JFK, though, being steeped in Massachusetts' history, may have borrowed from the Governor of the Massachusetts Bay Company when he addressed the Massachusetts legislature.
In any event, if anyone is interested, here are links to all the texts mentioned in this post.
Full text of Winthrop's sermon/speech/pep talk given on the ship Arabella, with an intro by Beardsley (that I recommend skipping):
http://religiousfreedom.lib.virginia.edu/sacred/charity.htmlStart of the sermon on the mount (Matthew, Chapter 5, KJV):
http://www.biblegateway.com/passage/?search=Matthew%205&version=KJV(If you want to read the entire sermon--highly recommended--you can easily search at the above site for Matthew Chapters 6 and 7, where the sermon on the mount continues, but the "city on a hill phrase is in Chapter 5).
JFK's 1961 city on a hill speech, video and transcript:
http://www.jfklibrary.org/Asset-Viewer/OYhUZE2Qo0-ogdV7ok900A.aspxReagan's 1974 city on a hill speech:
http://reagan2020.us/speeches/City_Upon_A_Hill.asp