I have faced it in the political news. For example here in the comments under the article:
What does it mean exactly and why is it called like this?
"Teabagger" is yet another shining example of "civil discourse" by left wingers in America.
The etymology of the word "teabagging" involves a slang term originating in American homosexual subculture (ref-NSFW) involving a specific (typically humiliating based on context) sexual activity between two homosexual males. I won't bother going into clinical details, for Urban Dictionary does that for you. The term first entered popular culture via a gay bar scene in a 1998 comedy/drama movie called "Pecker" and then video game players imitating the act.
The supposedly cultured, civil and enlightened members of left wing political culture (up to and including President Obama, who three days earlier publicly decried the lack of civility in American politics) and supposedly professional journalism (CNN and MSNBC main anchors and PBS senior correspondent, not just some random blogs or forum commenters) decided that this term would strongly elevate American civil discourse if it was publicly and massively applied to members of Tea Party (which was, of course, a political movement named after a famous historical event wherein a quantity of tea cargo was destroyed in protestation of British tax policies).
The nominal reason for this shining beacon of an example of civil, polite and dignified example of political engagement of one's opponents from the American left wing was the fact that Tea Party in 2009 advocated sending - in reminder of said Boston Tea Party - tea bags to elected officials as a "Taxed Enough Already" (TEA) sign.
(I'll try and post a less overtly biased and editorialized answer. We'll see how it flies...)
The term 'teabagger' is slang (typically used in the pejorative sense) to refer to those that associate themselves with the Tea Party, which is a movement primarily (but not exclusively) associated with the Republican Party in the United States.
It's a double entendre as it refers to a sex act/prank as well.
UPDATE: It appears some contest the statement that the Tea Party is primarily affiliated with the Republican Party. It's not necessarily germane to the question, but did offer some context as to where the Tea Party sits on the US political spectrum. That statement is based on the fact that of the 100+ US Politicians that claim affiliation with the Tea Party Movement, all are Republican. In addition, of the 66 members of the Tea Party Caucus in Congress, all were republican. As for supporters, per a Gallup poll, "Tea Party supporters are decidedly Republican".
Moreover, as Jay Nordlinger at National Review admits, the term "teabagger" was introduced to the political lexicon by Tea Party movement leaders:
The first big day for this movement was Tax Day, April 15. And organizers had a gimmick. They asked people to send a tea bag to the Oval Office. One of the exhortations was “Tea Bag the Fools in D.C.” A protester was spotted with a sign saying, “Tea Bag the Liberal Dems Before They Tea Bag You.” So, conservatives started it: started with this terminology. But others ran with it and ran with it. — (source)
"Teabagging" is when a male dips his scrotum upon another person's face as an insult. It's commonly simulated in FPS video-games where a victorious player crouches up and down over a player that he's killed.
In the scope of politics, It's a pejorative term for a member of the "Tea Party" which is a movement which is known for it's fiscal conservatism.
one uses the term "teabagger" is used to put extra emphasis on the fact that he/she doesn't take that particular member of the tea party seriously.
The reason they use the word "teabagger" is simply because both
Tea Party and
Teabag have the word
Tea in them