All 100 senators are meeting Monday night and Majority Leader Harry Reid is threatening to change the rules on how presidential nominees are confirmed. This could dramatically shift the way the Senate operates. The Post’s Ed O’Keefe explains. (The Fold/The Washington Post)

The Senate inched closer to an eleventh-hour deal late Monday night in a bid to avert an unprecedented maneuver to change the chamber’s rules governing presidential appointees, with nearly all 100 senators spending more than three hours huddled in a rare bipartisan, closed-door caucus.

Rank-and-file senators came out of the meeting reporting progress on the confirmation prospects of President Obama’s selections to head low-profile but influential agencies. Majority Leader Harry M. Reid (D-Nev.) echoed that sentiment but said no resolution had been reached, leaving in place a critical 10 a.m. Tuesday vote that would set up the historic clash over changing the Senate rules on a raw party-line vote so that Cabinet- and agency-level nominees could be confirmed without having to overcome a filibuster.

Republicans have threatened to retaliate on a host of other legislative matters, creating the possibility that the already toxic tensions in the chamber would hit new heights because of the move that some call “the nuclear option.”

Invoking the spirit of early-19th-century deals that delayed the onset of the Civil War, senators met in the Old Senate Chamber, which until 1859 served as the meeting room for such key pacts as the Missouri Compromise of 1820.

“There’s no deal but there’s a much better understanding,” said Sen. John D. “Jay” Rockefeller IV (D-W.Va.), one of his party’s most senior senators. Rockefeller said there was a framework for a possible deal before the showdown votes on Obama’s current picks to run the National Labor Relations Board and the Consumer Financial Protection Bureau. Some exited more grim, including Sen. John McCain (R-Ariz.), who spent the previous week in shuttle diplomacy with Reid, Minority Leader Mitch McConnell (R-Ky.) and the White House.

Highlights from Thursday’s debate over the future of the filibuster between Senate Majority Leader Harry Reid and Minority Leader Mitch McConnell on the Senate floor. (Sarah Parnass/The Washington Post)

Asked whether Reid had come around, McCain said simply: “Yes, sort of.” He said the talks were now firmly between Reid and McConnell, predicting a long night ahead.

McConnell did not speak after the meeting, issuing a statement declaring “a clear bipartisan majority” supported finding a solution.

Only two of the 100 senators missed the marathon meeting, because of personal commitments, and roughly three dozen senators spoke during the closed-door session. “I think everybody in there came away with a better appreciation for how the other side feels,” Sen. Jeff Flake (R-Ariz.), a freshman who sat alongside two Democrats, said afterward.

At the outset, Reid remained defiant Monday, saying that Republicans can avoid a showdown by backing off threats to block seven nominees slated for consideration.

“I love the Senate, but right now the Senate is broken and needs to be fixed. It’s time for course correction,” Reid said at the Center for American Progress, a think tank closely aligned with the Obama administration and congressional Democrats.

White House officials said the president had played a behind-the-scenes role in the messy procedural fight, saying that Obama supported Reid in whatever decision he made. At Reid’s urging, Obama has made calls to wavering senators asking them to back Reid if he makes the move.

“The Senate needs to confirm this president’s nominees in a timely and efficient manner,” White House press secretary Jay Carney told reporters Monday.

The dispute centers on Republican treatment of Obama’s nominees, particularly selections for the NLRB, the new CFPB and a couple of Cabinet posts. Republicans, holding 45 seats and enough to filibuster any nominee, have been refusing to confirm the selections for the NLRB and the CFPB because they were given interim appointments by Obama that have since been ruled unconstitutional by federal appellate courts. The case is heading for a Supreme Court ruling likely next year.

Sens. Orrin G. Hatch (R-Utah) and Richard J. Durbin (D-Ill.) agreed that the bulk of the conversations focused on those two agency posts. Hatch said Republicans appeared willing to confirm Cordray, but some GOP senators have been pushing for reforms to the CFPB in exchange for supporting him. Hatch remained steadfast in seeing two different Democratic selections for the CFPB, but Durbin said Democrats remained opposed to that.

Without a deal Durbin — his party’s chief vote counter — predicted Reid still had enough support to change the rules on party lines.

“We’re going to have a majority,” he said.

Democrats see these delays as part of a broader escalation of procedural obstruction that the GOP minority has used to slow down the confirmation of even nominees who eventually win broad bipartisan votes.

“The only people in power are the obstructionists,” Sen. Mary Landrieu (D-La.) said Monday evening, declaring her support for the filibuster rules change.

One aide to a Democratic senator, requesting anonymity to discuss the closed-door meeting, said that a senior Democrat told his Republican colleagues that they have disrespected the president with their treatment of his nominees. Reid in particular has focused on McConnell’s relenting to pressure from junior Republicans to allow brief filibusters of the confirmation of Chuck Hagel as defense secretary and John Brennan as CIA director.

Both those posts have traditionally been approved on large bipartisan votes in which no vote was even required to shut off the filibuster. McConnell has countered that Hagel and Brennan got confirmed, as has every other Obama Cabinet nominee, and he has signaled that Republicans will drop their objections to nominees to head the Labor Department and the Environmental Protection Agency.

At issue, however, is the means to changing the rules as much as it is the end result that Reid is demanding. It also goes to the heart of an intensifying debate about the heightened partisanship inside the Senate, which the Founding Fathers envisioned as the “cooling saucer” to the more partisan House.

Obscure to even most senators themselves, Reid’s party-line method for the rules change would overrule the chamber’s long-held standards that required a supermajority of 67 senators to sign off on such a big step.

“There’s a reason why it’s called nuclear,” Sen. Max Baucus (D-Mont.) said entering the meeting. Later, he said such a gathering was helpful for the broader Senate environment. “It was very refreshing. We learned a lot,” he said as he left the meeting early. “There should be many more meetings like that, frankly. We don’t talk to each other enough.”

Republicans warned that if they win back the majority in the 2014 midterm elections, they would use the party-line vote to simply abolish the filibuster on all legislation and then approve by a bare majority vote the repeal of Obama’s health-care law and anti-union legislation.

“I think there’s enough recognition on both sides that the shoe can be on the other foot rather quickly and that people in the majority today will be in the minority tomorrow, and vice versa,” said Sen. John Cornyn (R-Tex.), the chamber’s second-ranking Republican.

Reid hinted early Monday that the rules could change at a later date to perhaps allow legislation to pass with a simple majority vote. “Nothing right now. But remember, the Senate is an evolving body,” he said.

Both sides have switched their positions from where they were in the spring of 2005, the last time the Senate came this close to executing a partisan rules change. Then, Republicans held the majority and wanted to ram the Bush White House’s judicial nominees through without Democratic objections, and Reid led the fight on behalf of the filibuster, calling it the single most important thing he had done in his Senate career.

Reid’s first test vote Tuesday would come on Cordray’s nomination, needing 60 votes to move to a debate and final confirmation vote. Up after that would come the NLRB nominees, followed by less controversial selections to lead the U.S. Export-Import Bank, the EPA and the Labor Department.

“These are good people,” Reid said early Monday.

Jenna Johnson, Rachel Weiner and Philip Rucker contributed to this report.