Question: When did the party with majorities in Congress prior to the 1954 elections gain control of the body which determines rules of the US House and US Senate?

Knowledge 1: 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 2: Dwight D. Eisenhower
As the 1954 congressional elections approached, and it became evident that the Republicans were in danger of losing their thin majority in both houses, Eisenhower was among those blaming the Old Guard for the losses, and took up the charge to stop suspected efforts by the right wing to take control of the GOP. Eisenhower then articulated his position as a moderate, progressive Republican: "I have just one purpose ... and that is to build up a strong progressive Republican Party in this country. If the right wing wants a fight, they are going to get it ... before I end up, either this Republican Party will reflect progressivism or I won't be with them anymore." [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: 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 2: Dwight D. Eisenhower
As the 1954 congressional elections approached, and it became evident that the Republicans were in danger of losing their thin majority in both houses, Eisenhower was among those blaming the Old Guard for the losses, and took up the charge to stop suspected efforts by the right wing to take control of the GOP. Eisenhower then articulated his position as a moderate, progressive Republican: "I have just one purpose ... and that is to build up a strong progressive Republican Party in this country. If the right wing wants a fight, they are going to get it ... before I end up, either this Republican Party will reflect progressivism or I won't be with them anymore." [SEP] Knowledge 3: 115th United States Congress
The One Hundred Fifteenth United States Congress is the current meeting of the legislative branch of the United States federal government, composed of the Senate and the House of Representatives. It meets in Washington, D.C. from January 3, 2017, to January 3, 2019, during the final weeks of the Obama presidency and the first two years of Donald Trump's presidency. The November 2016 elections maintained Republican control of both the House and Senate.
Knowledge 1: 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 2: Dwight D. Eisenhower
As the 1954 congressional elections approached, and it became evident that the Republicans were in danger of losing their thin majority in both houses, Eisenhower was among those blaming the Old Guard for the losses, and took up the charge to stop suspected efforts by the right wing to take control of the GOP. Eisenhower then articulated his position as a moderate, progressive Republican: "I have just one purpose ... and that is to build up a strong progressive Republican Party in this country. If the right wing wants a fight, they are going to get it ... before I end up, either this Republican Party will reflect progressivism or I won't be with them anymore." [SEP] Knowledge 3: 111th United States Congress
The One Hundred Eleventh United States Congress was a meeting of the legislative branch of the United States federal government from January 3, 2009, until January 3, 2011. It began during the last two weeks of the George W. Bush administration, with the remainder spanning the first two years of Barack Obama's presidency. It was composed of the Senate and the House of Representatives. The apportionment of seats in the House was based on the 2000 U.S. Census. In the November 4, 2008, elections, the Democratic Party increased its majorities in both chambers, giving President Obama a Democratic majority in the legislature for the first two years of his presidency. A new delegate seat was created for the Northern Mariana Islands. The 111th Congress had the most experienced members in history: at the start of the 111th Congress, the average member of the House had served 10.3 years, while the average Senator had served 13.4 years. This Congress has been considered one of the most productive Congresses in history in terms of legislation passed since the 89th Congress, during Lyndon B. Johnson's Great Society.

Answer: January 2015