The reason for the urgency is that leaders believe Senate rules can only be changed with a bare majority vote on the first legislative day of a new Congress. Senate Majority Leader Harry Reid (D-NV) effectively extended the first day until the Senate reconvenes next Tuesday (by "recessing" rather than "adjourning" earlier this month on the actual first day). His office says the Senate won't technically be in session next Monday for the swearing-in ceremonies.
The "talking filibuster" proposal faces opposition from Republicans and longtime Democrats, chiefly Sen. Carl Levin (D-MI). He and Sen. John McCain (R-AZ) are pushing a competing scaled-back plan that would require the usual two-thirds majority to change the rules outside what Republicans call the "nuclear option." Reid has vowed to weaken the filibuster but hasn't clarified which proposal he's leaning toward, having praised both.
The Levin-McCain plan would make it easier for the majority to move to debate on legislation while guaranteeing the minority two amendments regardless of relevancy. It would also expedite some judicial nominations. Levin has warned his colleagues not to ram through a significant change to the rules without the consent of a two-thirds majority.
In recent weeks, Reid has been negotiating privately with Senate Minority Leader Mitch McConnell (R-KY) on a resolution that could avoid the constitutional option, while keeping options open. That's worrying the pro-reform coalition, which doubts McConnell would consent to anything that meaningfully curtails the Senate minority's power.
Sen. Chuck Schumer (D-NY), who was involved in the McCain-Levin negotiations, declined to take a stance on which proposal he prefers. But he said early this month that he wants as far-reaching filibuster reform as can be achieved.
Merkley and Udall claim the Levin-McCain plan would a step backward for the cause, arguing that the minority could use amendments to poison legislation.
"Other proposals out there don't go far enough," the petition reads, "and won't change the culture of obstruction that paralyzes the Senate."