One of the stranger impacts of the show occurred on January 31 , 2006 , when The West Wing was said to have played a hand in defeating Tony Blair 's government in the British House of Commons , during the so called `` West Wing Plot '' . One of the stranger impacts of the show occurred on January 31 , 2006 , when The West Wing was said to have played a hand in defeating a proposal backed by Tony Blair 's government in the British House of Commons , during the so called `` West Wing Plot '' .