The U.S. Senate failed Monday evening to resolve threats by Democrats to change the chamber’s rules governing presidential appointees, but several senators emerged from the rare closed-door meeting impressed by the exchange — and eager to do it again.

“It was a great debate; it was certainly one of the high points of my time here,” said Sen. Angus King (I-Maine), who joined the Senate in January. “Hearing people actually stand up and talk and actually make compelling arguments and listen and learn, it’s the way it ought to work.”

“We should do it more often,” said Sen. Kelly Ayotte (R-N.H.).

Only two of the 100 senators — Marco Rubio (R-Fla.) and Jeanne Shaheen (D-N.H.) — missed the marathon meeting because of personal commitments, and roughly three dozen senators spoke during the closed-door session that began shortly after 6 p.m.

Majority Leader Harry M. Reid (D-Nev.) and Minority Leader Mitch McConnell (R-Ky.) spoke first, followed by Sens. Lamar Alexander (R-Tenn.) and Richard J. Durbin (D-Ill.), according to senators. Then anyone could rise and speak, and most lined up in the aisles of the Old Senate Chamber to share their thoughts.

The old chamber, just down the hall from the current Senate Chamber, is an ornate room that was used from 1819 to 1859 when the issue of slavery dominated congressional discourse. It’s the room where senators agreed to the Missouri Compromise of 1820 and where, in 1830, Sen. Daniel Webster of Massachusetts sparred with Sen. Robert Y. Hayne of South Carolina over a state’s right to nullify federal laws. In the 1850s, elite Washingtonians who could afford the time would come to watch animated debates between Webster, Sen. Henry Clay of Kentucky and John C. Calhoun of South Carolina.

Today, the room is best known as the setting for the ceremonial swearing-in ceremonies for new senators and otherwise serves as a stop on official tours of the U.S. Capitol.

Several senators commented on how healthy it had been to talk to one another in private, away from television cameras and staff members. The tone was cordial and respectful, they said, lacking any blow-ups or shouting.

“There was no rancor at all,” said Sen. John Boozman (R-Ark.) He added later, “I think if the American people were watching, the whole tone would have been different. It’s different when the TV cameras are on. That might be part of the problem.”

“It literally kept going until every member who wanted to speak had had a chance to speak,” said Sen. Christopher Coons (D-Del.). “Frankly, if we did that more often, we would have a healthier Senate. The number of senior senators who spoke longingly about the way it used to function and of the importance of working together, and the number of junior senators who spoke positively about recent experiences partnering up on bipartisan legislation, created a generally positive atmosphere. And the number of expressions of regret about the possibility of doing something to affect or harm the institution, sort of moved it into a positive place.”

But there was angst in the room, according to Sen. Max Baucus (D-Mont.), who defined it this way: “Angst like, ‘Oh, my gosh, I hope that we don’t do something here that’s going to cause deeper partisanship, because we’re too partisan now.’”

Baucus spoke fondly of the private dining room, now closed, where senators used to eat lunch. Nowadays senators instead attend private caucus lunches several times a week, a practice he did not think was positive for the Senate.

Alexander agreed, saying that the weekly partisan lunches that divide the chamber by party at midday mean that senators “operate on different facts.” He called the meeting productive but lamented that younger colleagues still seem set on dramatically overhauling Senate procedure.

“I’m glad we had the meeting, I appreciate it, but there are too many senators who don’t understand the precedent of a Senate that can change the majority anytime it wants to, to do anything it wants to,” said Alexander of Tennessee.

The meeting also marked the final official act of Sen. William “Mo” Cowan (D-Mass.), who is poised to step down Tuesday to make way for Rep. Edward J. Markey (D-Mass.), who won a special election last month to take the seat of former senator John F. Kerry (D).

Asked what he thought about spending his last night as a senator locked inside a room with his colleagues, Cowan could only laugh: “When Mo Cowan comes to the Senate, interesting things happen,” he said.