The United States House of Representatives have been called “the People’s House” because of the direct election of representatives. Members of the United States Senate (the other branch of Congress) were selected by state legislatures until the Seventeenth Amendment to the Constitution (passed in 1913) allowed for their popular election.
 
The term “the People’s House” has been cited in print since at least 1824. Although senators have been elected by the people since 1913-14, the term “People’s House” is still used.
 
The White House is also often called “the people’s house.” The houses of several state legislatures have been called “the people’s house” as well.
 
 
Wikipedia: The People’s House
The People’s House is a colloquial term used to describe the institution of the United States House of Representatives.
 
The term comes from the populist characteristics of the House: smaller representative districts, shorter terms of office for its members and (perhaps most importantly) direct election by the people. The House of Representatives was the only branch of the Federal government to be directly elected by the people until ratification of the Seventeenth Amendment to the United States Constitution in 1913, when the Senate was made a directly-elected body.
 
The United States Capitol building, where the House of Representatives meets, is sometimes referred to as “the People’s House,” as well.
 
In the U.S. state of Vermont the state house is also called “the People’s House.”
 
United States House of Representatives
The United States House of Representatives is one of the two Houses of the United States Congress, the bicameral legislature which also includes the Senate.
 
The composition and powers of the House are established in Article One of the Constitution. The major power of the House is to pass federal legislation that affects the entire country, although its bills must also be passed by the Senate and further agreed to by the President before becoming law (unless both the House and Senate re-pass the legislation with a two-thirds majority in each chamber). Each state receives representation in the House in proportion to its population but is entitled to at least one representative. The most populous state, California, currently has 53 representatives. The total number of voting representatives is fixed by law at 435. Each representative serves for a two-year term. The Speaker of the United States House of Representatives, traditionally the leader of the majority party, is the presiding officer of the chamber, elected by the members of the House.
 
The Constitution grants the House several exclusive powers: the power to initiate revenue bills, to impeach officials, and to elect the President in case of an Electoral College deadlock.
 
The House meets in the south wing of the United States Capitol.
 
Google Books
14 February 1824, Niles’ Weekly Register, pg. 369, col. 2:
I have said that the popular will is paramount, in most cases. The enlarged powers of the house of representatives shews this—it is the people’s house, and the members of it hold the purse strings; and, that the people may appear in it, the elections are biennial.
 
Google Books
28 May 1825, Niles’ National Register, pg. 204, col. 1:
The house of representatives—the great depository of our rights and liberties—the people’s house—composed of their immediate agents, would have presented to the nation and the world the shameful and disgraceful spectacle, of balloting for a president without effect, from the 8th of February to the 3d of March, at midnight.
   
15 August 1883, Harrisburg (PA) Patriot, pg. 2, col. 2:
It is the house and not the senate that represents the popular will. It is the house that is close to the people. It is the people’s house that should have a controlling voice in the matter of apportionments, rather than the senate which does not so nearly represent the mass of the population.
 
Google Books
The American Plan of Government:
The Constitution of the United States as interpreted by accepted authorities
By Charles William Bacon and Franklyn Stanley Morse
New York, NY: G. P. Putnam’s Sons
1916
Pg. 156:
The two-year period for which Congress may make appropriations for the support of an army, was established probably because the members of the House of Representatives are elected every two years. The People’s House of each Congress must assume responsibility for the size of the army, since it has to take the first step toward making the biennial appropriation for its support.
 
Google Books
Our America:
Today & Yesterday
By Floyd Melvyn Lawson and Verna Kopka Lawson
New York, NY: D. C. Heath
1938
Pg. 277:
Since the House of Representatives was to be the people’s house, and since the people had to pay the taxes, all tax bills were to start in this lower house.
   
Google News Archive
6 August 1970, Tuscaloosa (AL) News, “Flowers From Washington” by Walter Flowers (Fifth District Congressman), pg. 24, col. 1:
Without exception, I think the people have a right to know how their elected representatives vote on any issue—particularly in the House of Representatives of the United States which has been so aptly called the “People’s House.”
 
24 June 1976, Christian Science Monitor, “U.S. House moves to mend its ways, tidy its fringes” by Peter C. Stuart, pg. 1: 
The internal reforms of the House of Representatives—which its members are fond of calling “the People’s House”—would be solidified by the replacement,...
 
New York (NY) Times
TURMOIL IN CONGRESS; Transcript of Wright’s Address to House of Representatives
Special to The New York Times
Published: June 1, 1989
WASHINGTON, May 31— Following is a transcript of House Speaker Jim Wright’s address to the House of Representatives, with Representative Thomas S. Foley, the majority leader, presiding, as recorded by The New York Times:
 
Mr. Speaker, for 34 years I have had the great privilege to be a member of this institution, the people’s house, and I shall forever be grateful for that wondrous privilege.
 
Google Books
American Government:
Historical, popular, and global perspectives
By Kenneth Dautrich; et al.
Boston, MA: Wadsworth Cengage Learning
2010
Pg. 163:
The House of Representatives: The “People’s House”
The Founders intended the House of Representatives to be the “people’s house,” or the institution through which ordinary people would be representated in government. At the time the Constitution was adopted, the only federal officials directly elected by the people were members ofthe House of Representatives. Senators were chosen by state legislatures; the president and vice president were selected by electors in the Electoral College; and judges, ambassadors, and high-ranking officials in the executive branch were nominated by the president and approved by the Senate. In Federalist No. 51, James Madison admonished, “As it is essential to liberty that the government in general should have a common interest with the people, so it is particularly essential that the branch of it under consideration [the House] should have an immediate dependence on and an intimate sympathy with the people.” The House of Representatives thus directly connects voter sentiment with popular representation.
 
National Review Online—The Corner
Boehner: ‘The People’s House’
January 5, 2011 8:44 A.M. By Robert Costa    
(...)
That’s how House Speaker-designate John Boehner will frame his mission later today in his first speech as speaker. In excerpts obtained by National Review Online, Boehner casts himself as a “humbled” leader who accepts the speaker’s gavel “cheerfully and gratefully.”
 
“The American people have humbled us. They have refreshed our memories as to just how temporary the privilege to serve is.  They have reminded us that everything here is on loan from them.  That includes this gavel, which I accept cheerfully and gratefully, knowing I am but its caretaker.  After all, this is the people’s House.  This is their Congress.  It’s about them, not us.  What they want is a government that is honest, accountable and responsive to their needs.  A government that respects individual liberty, honors our heritage, and bows before the public it serves.”
 
POLITICO.com 
John Boehner: ‘This is the people’s House’
By RICHARD E. COHEN & JAKE SHERMAN | 1/5/11 9:12 AM EST Updated: 1/6/11 6:41 AM EST
John Boehner was elected the 61st speaker of the House on Wednesday, ushering in a new era of divided government with humble words and a somber tone — but a clear pledge to bring conservative principles back to Congress.