To virtually eliminate the threat of a filibuster in the U.S. Senate, the majority party would need to have at least 60 members. This is because invoking cloture to end debate on most legislation requires a supermajority of 60 out of 100 senators. Without 60 votes, a filibuster can continue to block legislation

. Since the Senate has 100 members, having 60 senators from one party would allow that party to overcome the filibuster by invoking cloture and proceeding to a vote. This 60-vote threshold is a longstanding Senate rule designed to protect minority rights but effectively gives the minority at least 41 senators the power to block legislation by filibustering

. In summary:

• The Senate requires 60 votes to invoke cloture and end a filibuster on legislation.
• Therefore, a party would need a minimum of 60 members to virtually eliminate the threat of a filibuster on bills.
• If the majority party has fewer than 60 senators, the minority can sustain a filibuster and block legislation

This 60-vote rule is sometimes referred to as the "supermajority" or "cloture threshold" and is central to the Senate's current filibuster practice.