The Constitution cites only five requirements for Senate supermajorities, including impeachment convictions of presidents, but allows the House and Senate to set their own rules. Under long-standing resolutions, the Senate considers itself to be a "continuing body" whose parliamentary rules remain in effect unless a two-thirds supermajority votes to change them.
Here's a brief recent history of the Senate's rules disputes:
May 2005: A bipartisan "Gang of 14" agrees to work together to avoid blocking several judicial nominees selected by President George W. Bush. Senators who helped negotiate the deal included John Warner (R-Va.), Ben Nelson (D-Neb.) and Lindsey O. Graham (R-S.C.).
February 2010: Senate Majority Leader Harry M. Reid (D-Nev.) dismisses an effort by some Democrats to eliminate the filibuster, saying the chamber's procedures were designed to prevent the majority party from unilaterally changing the rules. Some junior Senate Democrats were pushing to change the rules to avoid GOP attempts to block nominations and legislation.
Early January 2011: Senate leaders use a parliamentary trick to leave the chamber in a state of suspended animation — in reality adjourned since Jan. 5 but officially considered in a long recess that's part of the same individual legislative day — until later in the month as they work out a proposed change in the rules.
January 22, 2011: The chamber makes its most significant rules change in 35 years by agreeing to speed up its work by limiting the use of the filibuster and dropping the confirmation process for about 400 federal agency nominees.
November 2012: Shortly after Election Day, Reid and McConnell begin sparring over several days on the Senate floor after the Democratic leader once again threatens to change the rules by eliminating the filibuster vote needed to formally begin debate on legislation. He would allow for a final filibuster vote, thus making the chamber run more efficiently.
December 2012: Showing how far some are willing to go to challenge what they consider arcane rules, a federal judge hears in a case about whether Congress is constitutionally required to pass legislation by a simple majority vote and whether the Senate’s filibuster rules violate such a requirement.
January 24, 2013: Reid and McConnell agree to a bipartisan compromise authored by a handful of senior senators. The new rules essentially short-circuit one filibuster vote during the “motion to proceed” to a bill, when the chamber begins considering legislation. Republicans had increasingly filibustered the motion to begin debating legislation to slow the passage of bills or block them.
July 26, 2013: In another near-meltdown, Republicans agreed to confirm several of President Obama’s executive branch nominees and, in exchange, Democrats agreed to leave existing filibuster rules in place. The agreement came after an unprecedented closed-door meeting of senators in the Old Senate Chamber.
Nov. 21, 2013: Senate Democrats voted to change the chamber's rules so that federal judge nominees and executive-office appointments can be confirmed by a simple majority of senators, rather than the 60-vote supermajority that has been required for more than two centuries. The change does not apply to Supreme Court nominees.