The "nuclear option" is a parliamentary procedure that is toxic because it "games" the system, so to speak.
The Constitution gives each chamber the power to create its own rules. One rule that the Senate has is that they have to vote to change the rules. Any vote taken in the Senate requires cloture, which is a vote to end debate and move to the final majority vote. Cloture requires a "super-majority" to pass, in this case 3/5ths or 60 votes. Therefore, a vote to change the rules requires 60 votes to end debate, and then 51 votes to pass the rule.
The "nuclear option" is a parliamentary trick to bypass the regular order described above. Essentially, one Senator makes a point of order declaring something to be true, such as that the filibuster no longer applies to budget resolutions but still applies to new legislation, for example.
Once the point of order is made, the Parliamentarian rules on the point of order. The Senate then votes to accept or reject the ruling of the Parliamentarian, which is a majority vote not requiring cloture, thus bypassing the 60 vote requirement to end debate. The Vice President in his role as President of the Senate, can override the Parliamentarian's ruling if necessary.
-PJ
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