Voters sent two very conflicting messages to politicians in Washington last November. Work together, they all-but screamed — even as they cast ballots for an even more divided and partisan government.

The result could be months of stalemate as President Obama and the newly empowered Republicans in Congress clash repeatedly in a search for political advantage before the presidential election in 2012.

But two senators – one Democrat and one Republican – are quietly trying to resist those pressures. Republican senator Saxby Chambliss of Georgia and Democratic senator Mark Warner of Virginia are assembling a group of colleagues who they hope will embrace moderation, compromise and a willingness to tackle problems that require bipartisan solutions.

So far, the pair said during a small briefing for reporters on Monday, they have assembled about 20 of their colleagues, equally split between Democrats and Republicans, for a series of informal conversations about moving forward. Their primary target: finding common ground on a serious, long-term plan to address the nation’s deficit.

“We’re not starting with folks on the far right or the far left taking shots at this,” Mr. Chambliss said. “We’re starting with a group that’s in the middle, and we’re growing out.”

They are an unlikely pair. The son of a minister, Mr. Chambliss came to the Senate in 2003 after eight years in the House that began during the 1994 Republican revolution. Mr. Warner made millions in the telecommunications industry and later served a term as Virginia’s governor. But in the two years since Mr. Warner arrived in Washington, they have formed a friendship forged out of a common interest: finding the middle ground.

And it is far from clear how they can succeed in an institution that seems increasingly consumed by the arguments on the fringe of both parties. The coalition they are building is starting with baby steps — there are no binding commitments or formal structures. Just a “cease fire,” Mr. Warner said, “on criticizing each other’s ideas.”

Mr. Warner has had some success in the past. As governor, his biggest legislative victory came after he convinced 17 moderate Republicans in the state’s House of Delegates to bolt from party orthodoxy to support his tax reform plan that raised $1.2 billion for the state’s coffers.

The numbers are far larger now, as Mr. Warner and Mr. Chambliss attempt to confront the nation’s debt. Both men plan to use the report of Mr. Obama’s recent debt commission as the framework for legislation they will introduce in January to get the conversation started.

“You’ve got 15 percent of GDP coming in on revenues and 24 percent going out on spending,” Mr. Warner said. “You don’t need a PhD in economics to understand that’s not sustainable.”

While the group has not committed to specific actions, Mr. Chambliss said they have agreed among themselves that everything should be “on the table” as they move forward. Several of the senators in the new coalition took to the floor last week to give speeches imploring their colleagues to get serious about the deficit.

One advantage, they said, are looming votes on raising the nation’s debt ceiling and passing a permanent budget bill. Both votes can be used as leverage to force lawmakers to move more quickly on a long-term solution to the deficit, Mr. Warner and Mr. Chambliss said.

At one point Monday, the senators were asked whether their new coalition resembles past bipartisan groupings of lawmakers. (The “Gang of 6” negotiated during the health care fight last year and the “Gang of 14” came together in 2005 over the issue of the filibuster for judges.) Mr. Chambliss was emphatic in his answer.

“We are not a ‘gang.’ Gangs run around Atlanta and L.A. and cause mischief,” Chambliss said, prompting chuckles from the reporters. “This is a group of concerned members of the United States Senate who realize that this country faces a dead serious problem and we’ve got to do something about it.”