After Winters angered Saxon, who in actuality was the Master, Saxon ordered one of the Toclafane to kill Winters. One immediately did so, firing a laser bolt that disintegrated the President on the spot. His death signalled the start of the Toclafane occupation of Earth. (TV: The Sound of Drums)
When the paradox machine allowing the Toclafane to exist was destroyed, the natural cycle took over and though most of the events that had taken place were reversed, it only rolled back time to a few moments after Winters' death, meaning that it still happened and Winters remained one of the few casualties of the Master's failed plot. (TV: Last of the Time Lords)
Pompous, arrogant, cynical and short-tempered, President Winters saw himself as the rightful Earth representative. He was antagonistic towards the British, declaring that they had elected an "ass" with Saxon as Prime Minister, and displayed what he saw as perfect patriotism, but was in fact textbook arrogance. The Toclafane regarded him as stupid.(TV: The Sound of Drums)
Behind the scenes Edit
When meeting the Toclafane, Winters referred to himself as "President-Elect", suggesting that he had recently won an election but had not yet been sworn in. However, during The Sound of Drums, he was referred to as "President" numerous times and by different characters. Moreover, his plane was designated as Air Force One, which would not be true were he merely the President-elect.
Unless American law differs in the Whoniverse, it is impossible for an individual to be called the "President-elect" in the spring. The term applied to the winner of the US presidential election during the brief period from Election Day in November to Inauguration Day on the following 20 January — well before the events of The Sound of Drums. Additionally, a President-elect has no official standing or duties until formally taking office and becoming President, so Winters being on his mission at all would be extraordinarily unlikely were he still only President-elect.
This reference to the "President-elect" was almost certainly a production error that can be jointly laid at the feet of the script editor, the writer and the continuity supervisor, since it only occurs once in the script.
The later introduction of Barack Obama to the Whoniverse opens the question as to whether in the fictional universe of Doctor Who, Obama was elected president in a standard election, or if he was initially elected as the vice-presidential running mate of Winters and succeeded to the office upon Winters' death (as per American law).