Senate Majority Leader Harry Reid signaled Tuesday that he would try to push ahead with a supplemental spending package to aid Superstorm Sandy victims even as debate continues on revisions to the Senate’s filibuster rules.

The $50.5 billion supplemental for relief from last fall’s storm is the first of several holdover items from the 112th Congress up for consideration that the Nevada Democrat cited on the floor Tuesday.

“The Senate will help our fellow Americans continue to recover from Hurricane Sandy before another similar disaster strikes,” Reid said.

“Once we complete that vital legislation, the Senate will take action to make this institution that we all love — the United States Senate — work more effectively. We’ll consider changes to the Senate rules,” Reid said.

He added, “Because this matter warrants additional debate, today we will follow the precedent set in 2005 and again in 2011 to reserve the right of all senators to propose changes to the Senate rules.”

In trying to move the Sandy bill before any filibuster rules changes, Reid will need unanimous consent from Republicans. Under normal circumstances under the rules in effect in the 112th Congress, legislative days would need to intervene before a bill could reach the floor without such an agreement. However, to preserve his options on rules changes, Reid will need to continue his plan to keep the first legislative day of the session open.

While it was not immediately clear whether Republicans would go along with Reid, the delay in passing the Sandy aid package on the House side caused a public relations backlash for Speaker John A. Boehner of Ohio and other Republicans, with GOP Rep. Peter T. King of New York suggesting at one point that Republican donors in the New York metropolitan area should withhold campaign contributions from Republicans opposing the package. But were Reid to act on the Sandy aid without unanimous consent agreement, he could have a procedural mess.

Reid said Tuesday that he plans to continue to extend the legislative day of Jan. 3 — the first day of the 113th Congress — until the situation with the chamber’s rules can be resolved. Reid has outlined several changes he would like to see, and Senate Democrats are expected to discuss the matter during the weekly policy luncheon Tuesday afternoon.

In adding that he’s ”hopeful and cautiously optimistic” about cutting a deal with Senate Minority Leader Mitch McConnell, R-Ky., on increasing the speed at which the chamber can move through its business, Reid is effectively conceding that he wants to jettison more substantial changes favored by some more liberal Democrats, including a possible way to eventually limit debate on legislation with fewer than 60 votes.

McConnell again dismissed the idea that the Senate’s rules are the problem Tuesday.

“The Senate isn’t functioning as it should, and it has nothing to do with a process that has served us well for a very long time,” McConnell said. “But if we work together and strive to avoid some of the bad habits that have developed around here, I truly believe that we’ll be able to achieve the kinds of solutions that have eluded us for the past four years.”

Outside groups generally favorable to Democrats made another renewed push for more substantial rules changes Tuesday, however. Leaders of several groups, including NAACP President Ben Jealous, issued statements shortly before Reid spoke on the floor.

“The American people are losing faith in our democratic political process. We need to act now and end silent filibusters that run rampant in the U.S. Senate,” Jealous said. “The American people deserve more transparency and accountability and to hear a full debate on issues that have such a profound impact on their lives.”

Other matters on Reid’s agenda that were held over from the last Congress are a five-year farm program bill, legislation to revitalize and restore solvency to the Postal Service and a measure aimed at reauthorizing the Violence Against Women Act. Those are all bills that passed the Senate but did not lead to agreement with the House.