Meaning of "tea party"

Solution 1:

You're looking for information on the Tea Party movement in US politics, which gets its name from the famous Boston Tea Party protest in the history of US independence.

Modern "tea partiers" lie to the far right of mainstream US politics, and are known for doggedly (some would say dogmatically) adhering to the tenets of fiscal and social conservatism. The original Tea Party resisted taxation without representation, and the current movement resists, well, just taxation.

On a linguistic note, I think originally, referring to the messy tea protest in Boston as a "party" was intentional irony, but I am not sure.

On the question of the orthography of the demonym: I personally haven't seen it written in the apostrophe-y form, only ever as "tea-partiers" (which again creates a light pun with "partiers" for a serious political party which is typically depicted as humorless by their opponents).