Former Virginia Senator George Allen's use of the "macaca" racial epithet is the first example I came up with of YouTube having a significant impact on politics.

Here's some information about that incident:

"George Felix Allen (born March 8, 1952) is a former Republican United States Senator from the Commonwealth of Virginia, and the son of former NFL head coach George Allen. Allen served Virginia in the state legislature, as Governor, and in both bodies of the U.S. Congress. Allen's re-election in the 2006 race seemed inevitable until he was brought down by a video that showed him using a racial epithet when talking to a staffer for his opponent, Democrat Jim Webb"...

On August 11, 2006, at a campaign stop in Breaks, Virginia, near the Kentucky border, Allen twice used the word macaca to refer to S.R. Sidarth, an Indian-American, who was filming the event as a "tracker" for the opposing Webb campaign. Macaca means "monkey" and is a racial slur; it is generally used in francophone African nations, which led to speculation that Allen may have heard the epithet from his mother, a Francophone who grew up in French-colonial Tunisia. Allen apologized and later said that he did not know the meaning of the word. In 2008, The Washington Post speculated that, were it not for this single utterance, Allen would have been a strong candidate for the 2008 GOP presidential nomination."...

[My italics added for emphasis]

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The video of Allen's comments were uploaded to YouTube where they quickly went viral. YouTube videos of Allen's "apology" also were viewed by a large number of people as were discussions by numerous television commentators about this incident.