Washington (CNN) - In a rare, private meeting with nearly all 100 senators Monday night, the upper chamber failed to come up with a deal to avert the so-called nuclear option—a partisan threat by Senate Majority Leader Harry Reid that would eliminate filibusters for executive-branch nominees.
But after the nearly four-hour meeting, senators said Reid and Senate Republican Leader Mitch McConnell are expected to keep talking before a Tuesday deadline.
“The night is late,” Reid told reporters, not long before 10 p.m. ET. “We've had a very good conversation. That conversation is going to continue tonight.”
Senators left Capitol Hill with a sense that a solution would be found soon, before the Senate votes Tuesday morning to proceed with two Cabinet member nominees and five appointees to agency posts. Republicans have stalled the confirmation process for months.
"I think this will come to a head tomorrow. It was a very, very good discussion,” said Sen. John Boozman, R-Arkansas. “I think this was a good step."
While Democrats control the Senate, they don't have the 60 votes necessary to break a GOP-led filibuster. Reid would use the “nuclear option” to change the rules in order to prevent filibusters of executive branch nominations, allowing them to be confirmed on a simple majority vote of 51.
The Nevada Democrat has been warning Republicans that if they continue blocking some of Obama's Cabinet and agency picks, he will make the drastic move without their consent. Such a move would bring sharp opposition from Republicans, who have threatened to block other legislation as a consequence.
As they exited the Old Senate Chamber, senators said a large chunk of their colleagues spoke at Monday night’s meeting, which was held in the iconic Old Senate Chamber at the request of Republicans.
Sen. Max Baucus, D-Montana, said there was a lot of “angst” in the room but described the meeting as “the most bipartisan discussion we’ve had in a long time."
According to Sen. Jay Rockefeller, D-West Virginia, the relations between Reid and McConnell were “very good.”
“They spent most of the time listening,” he added. While no deal was reached Monday night, the five-term senator said “there is a better understanding.”
“I felt like people were far closer together the further we went along,” Rockefeller said.
McDonnell’s spokesman, Don Stewart, said in a statement that “a clear bipartisan majority in the meeting believed the Leaders ought to find a solution. And discussions will continue.”
Sen. Mike Johanns, R-Nebraska, also said the mood remained “good.”
“We're all adults and professionals,” he said.
Republican Sens. John Cornyn of Texas and Bob Corker of Tennessee also said there was a willingness to let the leaders hunker down and resolve the issue. Asked if it was possible to avoid the nuclear option, Cornyn said, “I think it is. I think we’re in a little bit better position than we were before.”
Not everyone felt encouraged Monday night, however. Sen. Lamar Alexander, R-Tennessee, said he didn’t “feel very good” about the gathering.
"I'm glad we had the meeting, I appreciated it. But there are too many senators who don't understand the danger of the precedent of a Senate that could change the majority anytime it wants to, to do anything it wants to,” he said. “Imagine what we Republicans would do in a year-and-a-half if we were in the majority."
At issue is a disagreement over three of the nominees–two for the National Labor Relations Board and one to head the Consumer Financial Protection Bureau. They were tainted in the minds of Republicans because they originally had been nominated as "recess appointments" by Obama – even though senators said they were in session.
Republicans have remained steadfast against confirming them until the Supreme Court decides if the recess appointments were constitutional, something the high court is considering.
Reid and Sen. John McCain engaged in quiet negotiations over the weekend and got close to averting the nuclear option but failed to seal the deal, sources in both parties told CNN.
If Democrats proceed with the nuclear option, Republicans will protest the change by slamming the brakes on other action in the Senate, according to current and former senior Senate aides from both parties.
McCain told Reid he found the six Republican senators needed to join Democrats in breaking filibusters of the nominations, giving Democrats a key part of what they want: approval of Richard Cordray to run the Consumer Financial Protection Bureau.
In exchange, the president would have to agree to withdraw the two NLRB recess nominees: Sharon Block and Richard Griffin. The NLRB, which hears and rules on labor disputes, is one of the most politically polarized institutions in Washington.
But Reid told McCain he couldn't go along with the idea because they could not find replacements willing to go through what will surely be a politically rough nomination for an NLRB term that would be up in 2014, according to sources in both parties.
Should the Senate go ahead with the nuclear option, the poisoned atmosphere could stall passage of several important items moving through Congress like tax reform, judicial nominations, government spending bills and a debt ceiling increase. Even a relatively modest rewrite of student loan laws could be in jeopardy, meaning students headed to school this fall would have to pay higher interest rates.
But Democrats say the pain will only be temporary.
A top Democratic aide said, "The immediate aftermath will be messy. The GOP will shut down the Senate and they will keep it locked down until there are tangible impacts from inaction. Only then, when people start to realize that their lawmakers are not working on the farm bill, immigration, budget and other issues, will they pick up the phone and call their lawmakers."
While the measure would only apply to executive branch nominees, Republicans argue Democrats would try to expand the option to other votes.
Reid said the change he is proposing is "very minimal," applying only to Cabinet and executive branch positions.
"This is not judges, this is not legislation - this has allowing the people of America to have a president who can have his team in place," Reid said on NBC's "Meet the Press." "This is nothing like what went on" in 2005.
Appearing later on the same program, McConnell seemed to tamp down some of the spite. Three days after saying Reid would be remembered as the worst Senate leader ever, McConnell said Reid was "a reasonable man, he's a good majority leader."
- CNN's Dana Bash contributed to this report.