Question: When did the party Harlan and Stewart were affiliated with gain control of the body which determines rules of the US House and US Senate?

Knowledge 1: Dwight D. Eisenhower
Whittaker was unsuited for the role and soon retired. Stewart and Harlan were conservative Republicans, while Brennan was a Democrat who became a leading voice for liberalism. In selecting a Chief Justice, Eisenhower looked for an experienced jurist who could appeal to liberals in the party as well as law-and-order conservatives, noting privately that Warren "represents the kind of political, economic, and social thinking that I believe we need on the Supreme Court ... He has a national name for integrity, uprightness, and courage that, again, I believe we need on the Court". In the next few years Warren led the Court in a series of liberal decisions that revolutionized the role of the Court. [SEP] Knowledge 2: Standing Rules of the United States Senate
The Standing Rules of the Senate are the parliamentary procedures adopted by the United States Senate that govern its procedure. The Senate's power to establish rules derives from Article One, Section 5 of the United States Constitution: ``Each House may determine the rules of its proceedings... '' [SEP] Knowledge 3: 2014 United States Senate elections
The Republicans regained the majority of the Senate in the 114th Congress, which started in January 2015; the Republicans had not controlled the Senate since January 2007. They had needed a net gain of at least six seats to obtain a majority. They held all of their seats, and gained nine Democratic - held seats. Republicans defeated five Democratic incumbents:
Knowledge 1: Dwight D. Eisenhower
Whittaker was unsuited for the role and soon retired. Stewart and Harlan were conservative Republicans, while Brennan was a Democrat who became a leading voice for liberalism. In selecting a Chief Justice, Eisenhower looked for an experienced jurist who could appeal to liberals in the party as well as law-and-order conservatives, noting privately that Warren "represents the kind of political, economic, and social thinking that I believe we need on the Supreme Court ... He has a national name for integrity, uprightness, and courage that, again, I believe we need on the Court". In the next few years Warren led the Court in a series of liberal decisions that revolutionized the role of the Court. [SEP] Knowledge 2: Standing Rules of the United States Senate
The Standing Rules of the Senate are the parliamentary procedures adopted by the United States Senate that govern its procedure. The Senate's power to establish rules derives from Article One, Section 5 of the United States Constitution: ``Each House may determine the rules of its proceedings... '' [SEP] Knowledge 3: 110th United States Congress
The Democratic Party controlled a majority in both chambers for the first time since the end of the 103rd Congress in 1995. Although the Democrats held fewer than 50 Senate seats, they had an operational majority because the two independent senators caucused with the Democrats for organizational purposes. No Democratic - held seats had fallen to the Republican Party in the 2006 elections. Democrat Nancy Pelosi became the first woman Speaker of the House. The House also received the first Muslim (Keith Ellison) and Buddhist (Hank Johnson and Mazie Hirono) members of Congress.
Knowledge 1: Dwight D. Eisenhower
Whittaker was unsuited for the role and soon retired. Stewart and Harlan were conservative Republicans, while Brennan was a Democrat who became a leading voice for liberalism. In selecting a Chief Justice, Eisenhower looked for an experienced jurist who could appeal to liberals in the party as well as law-and-order conservatives, noting privately that Warren "represents the kind of political, economic, and social thinking that I believe we need on the Supreme Court ... He has a national name for integrity, uprightness, and courage that, again, I believe we need on the Court". In the next few years Warren led the Court in a series of liberal decisions that revolutionized the role of the Court. [SEP] Knowledge 2: Standing Rules of the United States Senate
The Standing Rules of the Senate are the parliamentary procedures adopted by the United States Senate that govern its procedure. The Senate's power to establish rules derives from Article One, Section 5 of the United States Constitution: ``Each House may determine the rules of its proceedings... '' [SEP] Knowledge 3: 114th United States Congress
The One Hundred Fourteenth United States Congress was a meeting of the legislative branch of the United States federal government, composed of the United States Senate and the United States House of Representatives. It met in Washington, D.C. from January 3, 2015, to January 3, 2017, during the final two full years of Barack Obama's presidency. The 2014 elections gave the Republicans control of the Senate (and control of both houses of Congress) for the first time since the 109th Congress. With 248 seats in the House of Representatives and 54 seats in the Senate, this Congress began with the largest Republican majority since the 71st Congress of 1929 -- 1931.

Answer: January 2015