Final answer:
To pass a motion to invoke cloture and end a filibuster in the U.S. Senate, 60 votes are needed, which is a three-fifths supermajority of the Senate body.
Step-by-step explanation:
The number of votes required to successfully pass a motion to invoke cloture and cut off unlimited debate (ending a filibuster) in the Senate is 60 votes. This supermajority is necessary to overcome a filibuster, where senators can extend debate indefinitely to delay or prevent a vote on a piece of legislation. Since the 1975 amendment to the Senate Rule 22, cloture can be invoked with three-fifths of the Senate, down from the previous two-thirds requirement. It should be noted that this requirement does not apply to judicial nominations, for which only a simple majority is needed for cloture, or to the annual budget reconciliation act, which has been used to pass significant legislation without the need for overcoming a filibuster.