Technically, you need a two-thirds vote in the Senate to change any of the chamber's rules. In practice, you actually don't need a two-thirds vote in the Senate to change the rules. You can do it with 51 votes. But it's considered a bit of a rude thing to do.
The middle ground in this debate has been given the name "the constitutional option": It argues that on the first day of a new session of Congress, you only need 51 votes to change the Senate rules, as each Congress has a constitutional right to make its own rules. That's the approach various Democratic senators are taking in their effort to reform the filibuster.
But Thursday was the first day of the 113th Congress. And it came and went without filibuster reform. So is filibuster reform dead?
Nope. Majority Leader Harry Reid is just making the first day of the session last far longer than the typical 24 hours:
The Senate is simply not working as it should… But I believe this matter warrants additional debate during the 113th Congress. And Senators deserve additional notice before voting to change Senate rules. So today I will follow the precedents set in 2005 and again in 2011. We will reserve the right of all Senators to propose changes to the Senate rules. And we will explicitly not acquiesce in the carrying over of all the rules from the last Congress. It is my intention that the Senate will recess today, rather than adjourn, to continue the same legislative day, and allow this important rules discussion to continue later this month. I am confident the Republican leader and I can come to an agreement that allows the Senate to work more efficiently.
The way this technically works is that Reid is "recessing" rather than 'adjourning" for the day. The Senate is a weird place. But the filibuster reform debate is still on the way. Reformers tell me that the expected deadline is Jan. 22, or thereabouts.