This parliamentary tactic was never conceived of by the Founding Fathers and is only possible because of the historical deference showed to the Senate Majority Leader.
The amendment tree is a metaphor for the chart that shows what amendments may be offered to a bill and in what order they will be considered.
A simple example would be if Senator A introduces an amendment to the legislation being considered by the Senate, this would be a “first-degree amendment.” If Senator B wants to amend Senator A’s amendment before it is acted on, this would be a “second-degree amendment.” Under the parliamentary procedures the Senate would have to vote on all of the second-degree amendments before it could vote on the first-degree amendments. There are various branches on the tree for these and other types of amendments.
Senate rules limit how many of these amendments may be pending at once – usually three, though that may increase depending on the parliamentary procedure a bill is being considered under.
By tradition, the Majority Leader is recognized first at the start of a debate. This enables the Leader, from time to time, to block the minority from offering any changes to a bill. To accomplish this, the Majority Leader fills the amendment tree with extraneous or meaningless amendments thereby blocking the introduction of any legitimate amendments by any other Senator (including those in his own party). It is a form of parliamentary obstruction used by the majority.
Majority Leader Reid is not the first to use this tactic, but he has used it more than any of his predecessors. Generally, the less secure a leader, personally or numerically, the more obstructionist he is.
The consequence – intended or not – according to Pennsylvania Republican Senator Arlen Specter, is to stifle debate and undercut Senate traditions. Said Specter in a speech to the Senate, “The facts show that [today] the Senate is realistically dysfunctional.”