From Wikipedia: Cloture

The debate about the filibuster is really a debate about cloture, what it takes to stop debate and go to a vote on a specific bill. 

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On 8 March 1917, during World War I, a rule allowing cloture of a debate was adopted by the Senate on a 76–3 roll call vote at the urging of President Woodrow Wilson, after a group of 12 anti-war senators managed to kill a bill that would have allowed Wilson to arm merchant vessels in the face of unrestricted German submarine warfare. This was successfully invoked for the first time on 15 November 1919, during the 66th Congress, to end a filibuster on the Treaty of Versailles.

The Senate's cloture rule originally required a supermajority of two-thirds of all senators "present and voting" to be considered filibuster-proof. For example, if all 100 senators voted on a cloture motion, 67 of those votes would have to be for cloture for it to pass; however if some senators were absent and only 80 senators voted on a cloture motion, only 54 would have to vote in favor. However, it proved very difficult to achieve this. The Senate tried 11 times between 1927 and 1962 to invoke cloture but failed each time. Filibuster use was particularly heavy by Democratic senators from southern states to block civil rights legislation.

In 1975, the Democratic Senate majority, having achieved a net gain of four seats in the 1974 Senate elections to attain a strength of 61 (with an additional independent senator caucusing with them for a total of 62), reduced the necessary supermajority to three-fifths (60 out of 100). However, as a compromise to those who were against the revision, the new rule also changed the requirement for determining the number of votes needed for a cloture motion's passage from those senators "present and voting" to those senators "duly chosen and sworn". Thus, 60 votes for cloture would be necessary regardless of whether every senator voted. The only time a lesser number would become acceptable is when a Senate seat is vacant. For example, if there were two vacancies in the Senate, thereby making 98 senators "duly chosen and sworn", it would take only 59 votes for a cloture motion to pass.

The new version of the cloture rule requiring three-fifths (60%) rather than two-thirds (66.7%) approval, which has remained in place since 1975, makes it considerably easier for the Senate majority to invoke cloture.[citation needed] Even so, a successful cloture motion on legislation is uncommon.

Bills considered under the reconciliation process established in 1974 (certain bills concerning spending and the budget) cannot be filibustered and therefore don't require a supermajority cloture vote.

The U.S. House of Representatives does not have a cloture procedure, since filibustering is not possible in that body.