Senate Majority Leader Harry Reid (D-Nev.) pulled a resolution on Libya off the floor Tuesday when it became clear that Republicans — including co-sponsors of the measure — would stage a filibuster to make a point about the larger deficit debate consuming Washington.

The Senate had canceled its scheduled July Fourth recess at the urging of President Barack Obama and Senate Republicans — both of whom wanted Congress to stay in town to debate the looming debt limit deadline. However, Reid instead planned to hold a series of votes on a long-stalled proposal to authorize limited military engagement in Libya as a way to fill floor time while debt and budget talks continued behind the scenes.

This approach didn’t appease Senate Republicans looking to send a message to Obama, who spurned a last-minute invite to meet with them last week. They also used the gambit to prove to constituents that they were serious about dealing with the debt.

“That is the reason that we’re back here this week during July recess,” Sen. Bob Corker (R-Tenn.) said Tuesday of the deficit talks. “We need to focus on the issue at hand. Just to speak about how dysfunctional the United States Senate is: We’re here over the debt ceiling … but instead of just focusing on the issue at hand … we’re going to focus on something possibly that is irrelevant and has nothing whatsoever to do with [the budget] just to make the American people think that we’re doing something.”

Corker is a vocal opponent of the White House’s handling of the Libya mission, which began in March. He opposed the resolution when it cleared the Senate Foreign Relations Committee last week.

Though the Libya measure has bipartisan support and was on track to be the first successful Congressional action since military engagement began in the region, Democrats moved Tuesday afternoon to a symbolic Sense of the Senate resolution declaring, “Any agreement to reduce the budget deficit should require that those earning $1,000,000 or more per year make a more meaningful contribution to the deficit reduction effort.” The measure is intended to make Democrats’ point that tax breaks for the wealthiest Americans should be eliminated, but the nonbinding resolution does not call for any specific tax changes.

“The most important thing for us to focus on this week is the budget, so we’ll work to set up a vote on the Sense of the Senate resolution that I have offered on shared sacrifice and perhaps the Republican alternative, as well,” Reid said on the floor.

Republicans had no specific plans ready for an alternative Tuesday evening, but they could offer amendments to the measure if it is not filibustered on the floor.

Reid noted that he was “confident everyone knows the White House is involved” in the ongoing talks and meetings regarding a budget agreement necessary to pass an extension of the nation’s debt limit. Obama announced Tuesday that he had invited Congressional leaders from both parties to the White House for another meeting on the issue Thursday, with the intention of working out a final agreement to raise the debt ceiling and reduce the deficit in the next two weeks. White House Press Secretary Jay Carney said the president does not plan to accept an earlier invitation from Reid to meet Wednesday with Senate Democrats. “Thursday is the next meeting we anticipate,” Carney said.

The Majority Leader’s statements on the floor Tuesday evening marked the end of a chaotic day, which began with Democratic leadership aides confident that they had the votes to stave off a filibuster on the Libya resolution.

Sen. John McCain (R-Ariz.), for example, was a chief co-sponsor of the measure with Foreign Relations Chairman John Kerry (D-Mass.), and Democrats were confident they would keep a core group of GOP supporters who have been ardent in their stance on the war.

But as the day wore on, Republican Senators such as Corker, Libya detractor Dick Lugar (Ind.) and Budget ranking member Jeff Sessions (Ala.) spoke out against moving to the resolution, and the GOP appeared to pick up momentum for scuttling the vote in favor of highlighting its desire for debate on the debt limit.

After some scrambling, Democrats began conceding that they wouldn’t have the votes Tuesday to pass the resolution.

Republicans and Democrats alike are still confident they can do what the House couldn’t — pass legislation authorizing military action in Libya, even though the White House has said it doesn’t believe such authorization is necessary.

“The majority of Senators understandably prefers to focus on [the budget] issue this week, and therefore, consideration of the resolution authorizing force in Libya has been delayed,” McCain said in a statement. “I believe the Senate has a responsibility to debate the ongoing conflict in Libya, and it is my hope that we will address this issue as early as next week.”

Congress faces an Aug. 2 deadline to raise the government’s borrowing capacity, or the country risks default on its obligations.