For evidence of just how close the Senate has come to seizing up, consider the forum chosen by its leaders to conduct a last-ditch search for a restorative tonic.

For totally different reasons, Democrats and Republicans alike view the Senate as so thoroughly broken as to endanger its central role in the functioning of American democracy — which for 224 years now has put a premium on legislative transparency. But they could all agree that their final opportunity to make the situation a bit more tolerable had no chance of success unless a meeting of 100 minds took place in secret.

Filibuster after filibuster may make the north side of the Capitol look like a place created with perpetual impasse as the intended result. But at least the bitterness, blame-casting and distrust that attends the dysfunction is laid bare for all to see. Except in the rarest cases involving national security, the Senate gallery has always been wide open to the public and the press.

Not this time. Voters and reporters had no chance of being inside the Old Senate Chamber on Monday night when all senators were invited to file in. Majority Leader Harry Reid, D-Nev., and Minority Leader Mitch McConnell, R-Ky., concluded the two sides would never reach an understanding of one another’s complaints, let alone an agreement that stops the countdown clock on the “nuclear option,” unless the preening and pontificating could be minimized and too-rare bipartisan face time could be maximized.

And that meant gathering out of public view — especially not in the sight lines of the television cameras, which at the end of this month will have been providing gavel-to-gavel coverage of the Senate floor for 27 years.

One night of very undemocratic secrecy, in other words, would be worth it if the result is a revival of democracy in action.

In one sense, that rationale sounded like the congressional equivalent of one of the most infamous lines from the Vietnam War:  The unnamed American general who captured the absurdities of that conflict for so many when told an Associated Press reporter that his men “had to destroy the village in order to save it.”

One difference between that manifestly flawed 1968 Tet Offensive rationale and the situation in today’s Congress is this: Convening in the Old Senate Chamber has produced the desired result at least half the time — which is to say, once.

That undeniable success came in January 1999, when rapidly rising distrust and suspicion threatened to turn the impeachment trial of President Bill Clinton into a protracted and lurid circus that would have severely tarnished the Senate’s reputation for dignity and deliberation.

During two and half hours behind the old chamber’s locked doors, though, both liberal Democrats (with Edward M. Kennedy as their spokesman) and conservative Republicans (Phil Gramm representing them) learned that their shared interest was in bringing the proceedings to a decorous but relatively quick conclusion.

Since the event was labeled a joint gathering of the two caucuses, not a formal meeting of the Senate, what happened inside was treated like any other negotiating session at the Capitol: The deliberations weren’t recorded or made official in the Congressional Record. Rather, the agreement on trial procedures hatched out of public view was unveiled later on the Senate floor, debated with the outcome already assured and put to a roll call vote.

It was adopted 100-0, a mark of success that had seemed wholly unattainable this time.

A more recent meeting in the old chamber is tougher to quantify.

In January 2007, on the opening day of the 110th Congress, Reid and McConnell, both just starting in their current roles, gathered their colleagues in the 19th-century chamber for what was described afterward as a genial conversation about the mutual benefits of more bipartisanship and less bickering.

Two years, one presidential election and one Great Recession later, many Democrats and a few Republicans said memories of that day helped sustain the Senate through the most intense days of the campaign and the financial crisis. Without such a session, they suggested, the collaboration needed to prevent an economic calamity might have proved elusive.

But that sentiment is so five years ago. Which is why senators on Monday traveled even further back in time.

The room, where their predecessors met from 1810 to 1859, has been meticulously restored to its red-velvet, wood-stove, coffered-ceiling glory days, and it’s a favorite stopping place on every staff-led tour. (It’s also been made so soundproof that it’s been deemed suitable for several top-secret intelligence briefings and a pair of executive sessions to debate sensitive international matters, a trade deal with China in 1992 and an arms control pact with Russia in 2010.)

The hall’s past, however, doesn’t make it a harbinger to forestall a divisive standoff. A chance to witness the impassioned rhetoric about slavery was the hottest ticket in Washington in the 1850s, and those debates gave rise to the Senate’s reputation as the world’s greatest deliberative body.

All such noble talk, of course, could not prevent the Civil War.