Norquist grew up in Weston, Massachusetts. He is the son of Carol (nee Lutz) and Warren Elliott Norquist (a vice president of Polaroid Corporation), and is of Swedish ancestry. His brother, David Norquist has served in senior posts in Republican administrations at both the United States Department of Defense and the United States Department of Homeland Security. Norquist became involved with politics at an early age when he volunteered for the 1968 Nixon campaign, assisting with get out the vote efforts.

Norquist is best known for founding Americans for Tax Reform (ATR) in 1985, which he says was done at the request of then-President Ronald Reagan. Referring to Norquist's activities as head of ATR, Steve Kroft, in a 60 Minutes episode that aired on November 20, 2011, claimed that "Norquist has been responsible, more than anyone else, for rewriting the dogma of the Republican Party."  The primary policy goal of Americans for Tax Reform is to reduce government revenues as a percentage of the GDP. ATR states that it "opposes all tax increases as a matter of principle." Americans for Tax Reform has supported Taxpayer Bill of Rights (TABOR) legislation and transparency initiatives, while opposing cap-and-trade legislation and efforts to regulate health care.  In 1993, Norquist launched his Wednesday Meeting series at ATR headquarters, initially to help fight President Clinton's healthcare plan. The meeting eventually became one of the most significant institutions in American conservative political organizing. The meetings have been called "a must-attend event for Republican operatives fortunate enough to get an invitation", and "the Grand Central station of the conservative movement." Medvetz (2006) argues that the meetings have been significant in "establishing relations of...exchange" among conservative subgroups and "sustaining a moral community of conservative activists."  As a nonprofit organization, Americans for Tax Reform is not required to disclose the identity of its contributors. Critics, such as Sen. Alan Simpson, have asked Norquist to disclose his contributors; he has declined but has said that ATR is financed by direct mail and other grassroots fundraising efforts. According to CBS News, "a significant portion appears to come from wealthy individuals, foundations and corporate interests."

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