Arthur Winters

Arthur Coleman Winters was the President of the United States of America circa Spring 2008. After "Harold Saxon" announced the existence of the Toclafane to the world, Winters served as designated United Nations ambassador to the Toclafane.

After Winters angered Saxon (actually the Master), Saxon ordered Winters killed by one of the Toclafane. His death signaled the start of the Toclafane occupation of Earth. (DW: The Sound of Drums)

The Paradox Machine only rolled back time to a few moments after Winters' death, meaning that it still happened. (DW: Last of the Time Lords)

Barack Obama succeeded Winters, though it was not clear whether he was Winters' direct successor.

Behind the scenes
Also, unless American law differs in the Whoniverse, it is impossible for an individual to be called the "President-elect" in the spring. The term applies to the winner of the US presidential election during the brief period from Election Day in November to Inauguration Day on the following 20th January — well before the events of The Sound of Drums. 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.
 * Upon meeting the Toclafane, Winters refers to himself as "President-elect", suggesting that he has recently won an election but has not yet been sworn in. However, during The Sound of Drums, he is referred to as "President" numerous times and by different characters (the Doctor, "Saxon", Trinity Wells and others) and once time is reset near the end of Last of the Time Lords, UNIT can be heard over the radio saying they've just seen "the President" killed. Moreover, his plane is described as Air Force One, which would not be true were he merely the President-Elect.
 * See the discontinuity pages for The Sound of Drums and The End of Time'' for attempts to make narrative "sense" of this error.