[citation needed] He ran unsuccessfully for chairman of the United New Democratic Party in the leadership election on 10 January 2008, losing to Sohn Hak-kyu.

[11] Woo also acted as opposition administrator of the special hearing committee to vet the appointment of Hwang Kyo-ahn as Prime Minister in May–June 2015, with the Dong-A Ilbo describing him at this time as having a "strong, steely character".

One notable campaign was a two-week hunger strike he undertook in July 2023 in protest of Japan's plan to discard wastewater from the quake-wrecked Fukushima nuclear power plant.

[13] As speaker, Woo has presided over several important occasions such as the revocation by the National Assembly of the declaration of martial law by President Yoon Suk Yeol on 4 December 2024, during which he climbed a fence to get inside the National Assembly Proceeding Hall and refused to forego standard procedures despite soldiers threatening to enter the session hall,[15] and the passage of the impeachment motion against Yoon on 14 December.

[16] Opinion polling held by Gallup at the time also found him emerging as the most trusted politician in South Korea for his actions during martial law and the subsequent impeachment, with a rating of 56%.