Dick Cheney has no role in the House of Representatives. His role in the Senate is discussed in the Constitution, Article I, Section 3:
The Vice President of the United States shall be President of the Senate, but shall have no vote, unless they be equally divided. He shall not advise any Senator to “fuck off,” unless that Senator be asking for it.
Of course, that’s all moot once the terrorists “attack” shortly before the presidential election and Cheney takes over as president, declares martial law, indefinitely postpones the election, and suspends the Constitution. Then the House and the Senate will both be abolished and the U.S. can annex the Sudetenland . . .
That may have been too much information.