In the current Garland case, I said above that it “might” take 60 votes to end a filibuster. Current Senate rules require 60 votes to break a filibuster on a Supreme Court nomination, but that rule hangs by a fairly thin thread. All nominations used to be susceptible to a filibuster that required 60 votes for cloture. And Senate rules require a two-thirds vote to change a rule. But, in 2014, when the Democrats controlled the Senate majority (but less than two-thirds), they used their control to exercise what was called the “nuclear option.”
The theory behind that tactic was that a rule could be appealed to the chair of the Senate (either the vice president, if present, or a member of the majority party) and, if that chair rules something permissible, that evades the need for a two-thirds majority to vote to change the rule. This has been used rarely, and is called the “nuclear option” because it is like dropping a powerful bomb on the minority party, at the risk of blowing up Senate comity on other matters.