Fed up and rueful, Harry Reid, the Senate majority leader, made a startling admission on Thursday: he should have reined in the filibuster rule last year, when he had a chance. As Republicans engaged in yet another of their endless filibusters on what should have been a routine matter — reauthorizing the Export-Import Bank — Mr. Reid took to the floor and praised two senators for being right last year when he was wrong.

Tom Udall of New Mexico and Jeff Merkley of Oregon were prophetic in wanting to change Senate rules, he said. “The rest of us were wrong, or most of us, anyway,” he added. “What a shame.”

Since 2007, Democrats have been forced to try to break Republican filibusters 360 times — by far the highest rate in Congressional history. Ending them requires Democrats to get over a 60-vote hurdle. If Mr. Reid helped enact the proposal of the two senators, he would instantly make Congress more efficient and more democratic.

The plan would prevent the filibuster from being used abusively, without eliminating an important tool to give a minority party a voice. Among other changes, filibusters would require 10 senators to start, and members would have to speak continuously on the floor to keep it going. In current practice, a single senator can simply declare a filibuster against a measure. This rule change could have been enacted on a simple majority vote on the first day of the session. But Mr. Reid and other Democrats did not want to lose the ability to obstruct the Republican agenda if they lost control of the chamber.