Senate institutionalists were the clear winners Tuesday, when the chamber averted a Democratic threat to end filibusters on executive branch nominees.

Unlike some past handshake deals to avert a procedural crises, this one might actually have a chance because senators seem more invested in the agreement after holding a three-and-a-half-hour long meeting to share their heartfelt feelings about why the filibuster is or isn’t a good thing.

For instance, Sen. Lindsey Graham, R-S.C., conceded that there were problems with the GOP’s recent attempt to block nominations in an effort to force changes in law or make an agency impotent. That was the issue with the delay in confirming Richard Cordray to head the Consumer Financial Protection Bureau. Cordray ultimately got confirmed, 66-34, on Tuesday evening.

Graham was among the Senate Republicans involved in conversations throughout the weekend that led to Tuesday’s deal.

In effect, Graham disavowed a previous letter from all Senate Republicans that said no one should be confirmed to helm the CFPB until changes were made to the agency. Critics called such a move “nullification” since the organizational structure of the CFPB essentially required a confirmed director to fully function.

A Tuesday morning test vote on Cordray received 17 votes from the GOP side, after discussions that involved Sen. Rob Portman, a Republican from Cordray’s home state of Ohio.

“I also admitted I think what we had done on Cordray and a few others was — was out of bounds too. So, I mean clearly the NLRB needs to exist, so those of us who want to drive it in the ground, that’s not a good use of appointment power,” Graham said.

“My concern was the NLRB picks were chosen in a way that I think was an affront to the institution,” Graham continued in a reference to the use of recess appointments to seats on the National Labor Relations Board. President Barack Obama also used his recess appointment power to install Cordray at the CFPB, but as part of the deal to avoid the nuclear option, Obama and Senate leaders agreed to choose different nominees to fill the NLRB seats.

Avoiding a move by Senate Majority Leader Harry Reid, D-Nev., to change precedent on filibusters of executive branch nominees is good news for anyone worried about a move toward a majoritarian Senate, but reformers clearly have had an effect on the proceedings. The Senate wouldn’t have found itself on the brink of changes without Reid having the 51 votes needed to implement the changes.

That follows a key argument of the 2007 book “Filibuster: Obstruction and Lawmaking in the U.S. Senate” by Eric Schickler and Greg Wawro.

“We likened the filibuster to a war of attrition in our book; in such a contest, when the majority shows that it is committed to standing firm — even to the point of showing its willingness to carry out a rules change — the leverage shifts from the obstructive minority to the side with more votes,” Schickler and Wawro wrote Tuesday.

Reid brought Democratic Sens. Tom Udall of New Mexico and Jeff Merkley of Oregon with him to a media availability with reporters following the weekly party caucus luncheon on Tuesday in an obvious nod to the effect their push for rules changes had on the entire episode.

“It has become evident to all that the Senate has gone from being a ‘cooling saucer,’ as envisioned by George Washington, to a deep freeze, paralyzing our government’s ability to get things done,” Merkley said. “Today’s agreement to confirm President Obama’s team is a historic step toward restoring the Senate to what it should be.”

Health, Education, Labor and Pensions Chairman Tom Harkin of Iowa had said Monday that he would protest any deal that required the nominations of recess appointees Richard F. Griffin Jr. and Sharon Block to be withdrawn.

On Tuesday when that exact scenario played out, Harkin struck a different tune, saying that he was confident Griffin and Block would find somewhere else to go.

“I made no secret of my support for changing the rules,” Harkin said. “Some of you may also know that I have said before that I have mixed emotions about changing the rules in the middle of the game. So I had a little bit of ambivalence there. I think the rules should be changed, but I am also concerned about changing them now. They should be changed at the beginning of a Congress and a number of people said that last night.”

“So all in all everyone is going to get through,” Harkin said, noting that the deal includes Thomas E. Perez to be Secretary of Labor.

Senate Republicans have argued as part of a lawsuit that the two original NLRB picks were granted recess appointments when the Senate was not in recess. Two federal appeals courts have agreed with the GOP, and the Supreme Court has agreed to hear the case next term.

As much of a long shot as it may have seemed, the Monday night meeting likely helped senators see where the other side was coming from. Sen. Lamar Alexander, R-Tenn., said following Monday night’s marathon joint meeting in the Old Senate Chamber that he believed some Democrats didn’t have the facts right about blocking of executive and judicial nominations through filibuster, suggesting that while some are delayed, they’re usually eventually confirmed.

Merkley was among many senators who pointed to Monday night’s meeting as bringing about a deal to avert the crisis. He said he got a slightly different perspective after listening to Alexander make his case.

“Lamar Alexander stood up last night and he put the numbers forward in a very different fashion, primarily looking at judicial work. And the gist of his statistical number were to say that maybe the Senate hasn’t changed as much as you think,” Merkley said.

“There is a phrase from Kipling in the poem ‘If,’ ‘Trust yourself when all men doubt you, but make allowance for their doubting too.’ I think that that is a very good quality in a legislature, for us to listen to each other, have confidence in our own views, but also be willing to explore, listen to and ponder the points being made by out colleagues,” Merkley added.

Senators may have more opportunities to talk. Reid said he hoped to have more bipartisan meetings in the future, including one featuring two former leaders: Democrat George Mitchell of Maine and Republican Trent Lott of Mississippi.

Lott told CQ Roll Call that he would welcome the invitation.

“We’ve talked a little bit about that, and I think that’s a good idea, and I’d certainly be glad to participate” Lott said. He said he was in the Capitol for an event honoring the Finance Committee’s bipartisan work.

Humberto Sanchez contributed to this report.