WASHINGTON (Reuters) - Call it a humble effort to douse the flames of dysfunction and paralysis in the U.S. Senate.

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Frustrated by an inability to get much done amid the partisan rancor in what has been called "the world's greatest deliberative body," two senators - Republican Lamar Alexander and Democrat Mark Warner - have decided to quietly reach across the political divide.

They helped pull together a loosely organized group of senators - dubbed the "Volunteer Fire Department" by Republican Senator Lindsey Graham - to have private dinners and try to build relationships to help quell conflicts.

"The idea is basically this: When the Senate runs off the track, when there's a fire, when there's a problem, somebody rings the bell and everybody who can shows up to try to fix it," Alexander told Reuters. "Then we all go back to our usual role."

For months, small groups of senators have been meeting regularly for dinner at the exclusive Alibi Club, in a 19th-century town house in downtown Washington.

Alexander and Warner are members of the 100-year-old club, a place where presidents, senators, and other power brokers have socialized for generations.

If it all sounds a bit too naive and idealistic in an election year when bitter partisanship is the norm and a huge showdown over taxes, spending and debt is looming at the end of the year, consider this: It might be working, at least a little.

Senators who have attended at least one of the dinners credit the events for encouraging Democratic and Republican leaders to work through an impasse over scheduling votes on the confirmation of federal judges.

The dinners also helped prompt Democrats who lead the Senate to commit to a standard appropriations process this year and schedule votes on individual spending bills, rather than vote on one massive bill that would have little chance of approval, the senators said.

Whether that will improve the chamber's ability to produce a comprehensive spending plan is unclear. Last week, Republicans complained that Democrats are abdicating their responsibility to get a budget plan through the Senate.

It is also not certain whether efforts such as the Alibi Club dinners will make a dent in easing tensions in the big legislative battles ahead.

But, Warner and Alexander say, they have to start somewhere.

Beyond being a search for moderation and compromise in an increasingly polarized Senate, the "Fire Department" dinners amount to a recognition that most members of Congress simply are not as close to one another on a personal level as those from past generations.

Most members no longer live in Washington year-round.

Many head back to their home states on weekends, making it difficult for lawmakers to get to know one another and form the kinds of friendship and understanding that had long helped members of Congress bridge differences and pass legislation.

Many of today's lawmakers are the products of state redistricting plans that legislatures designed to make congressional districts more solidly in favor of one party or the other.

That has helped to reduce the number of politically moderate lawmakers in Congress - the ones who typically help to foster compromise.

'PURELY A SOCIAL EVENING'

At the "Fire Department" dinners there are no staff members, no lobbyists and no hangers-on. Just senators, although spouses occasionally have joined the group.

About 75 of the 100 U.S. senators have attended at least one of the four dinners, by Warner's count. The guest lists are strictly bipartisan - half the guests are invited by Warner and the other half by Alexander.

"It's purely a social evening," Alexander said. "We sit around a big table and we talk about the work we're doing and have a good time getting to know each other better."

Graham called the dinners a way to spend some "down time" with colleagues and to get to know them in a way that "I just think is going to pay dividends."

Under Senate rules, a lone member can slow down deliberations on a bill and essentially bring the chamber to a standstill. The Senate can spend weeks in contentious debate on bills that never pass.

"There have been several times where the Senate spirals out of control, people get mad and in the heat of the moment they start pushing some pretty controversial things," Graham said.

He cited heated procedural dispute last year between Senate Democratic leader Harry Reid and Republican leader Mitch McConnell over a bill on currency manipulation by China. Reid angered Republicans by using an unprecedented maneuver to thwart an effort by McConnell to force votes on some amendments that were not relevant to the bill.

The frustration over such conflicts was evident earlier this year when Senator Olympia Snowe, a Republican who is among the dwindling number of lawmakers who could be considered politically moderate, announced that she would not seek re-election in part because of the increasing polarization in the Senate.

"We'll still have our disagreements on policy issues," Alexander said. "But we want to have a chance to bring important bills up, to debate them and amend them and, whenever we can, get a result."

The dinners at the Alibi Club, he and Warner said, can only help.

"We have great conversations and great evenings, and hope to continue to do more," Warner said.

Alexander said he does not want to exaggerate the role of the group, calling it a "modest step" toward improving relations in the Senate.

"If we overstate its importance," he said, "it will get less done."