The three were pushing for regulations on the treatment of American military prisoners, including a contentious ban on "cruel, inhuman or degrading treatment or punishment." The vice president wanted the provision pulled from a huge military spending bill. The senators would not budge.
"We agreed to disagree," Mr. Graham said in an interview last week.
That private session was an early hint of a Republican feud that spilled into the open last week, as Senate Republicans openly challenged President Bush on American military policy in Iraq and the war on terrorism. In the center of the fray, pushing Congress to reassert itself, were those same three Republicans.
Though their views on the war differ, they have much in common: each is a member of the influential Senate Armed Services Committee, each has a strong maverick streak and each has personal ties to the military - and to one another, mostly through Mr. McCain.
Senator Warner, the committee chairman and a veteran of World War II and the Korean War, was secretary of the Navy when Mr. McCain's father commanded the armed forces in the Pacific and Mr. McCain was a prisoner of war in Vietnam. That experience, he says, "bonded me with John McCain."
Senator Graham, a former military lawyer, was co-chairman of Mr. McCain's 2000 campaign for president in South Carolina and still has bitter memories of the tactics used by operatives for Gov. George W. Bush. Should Mr. McCain make a White House bid in 2008, as is widely expected, Mr. Graham says he will be there.
Their relationships with Mr. Bush are respectful, though not especially close, and each has a different political agenda. Mr. Warner, 78, aspires mostly to maintain his status as an elder statesman in the Senate. Mr. McCain, 69, covets the White House. And Mr. Graham, 50, is still a rising star.
But their "little triumvirate," as Mr. Graham calls it, has become a powerful political force at a time when President Bush's popularity is sinking and all of Washington is consumed with debate over the direction of the war in Iraq.
On that score, the three are not in lockstep. Last week, Mr. Warner prodded the Senate to require the Bush administration to provide Congress with quarterly progress reports on the war, spawning a raucous House debate over whether troops should withdraw and setting the stage for Iraq to dominate the 2006 midterm elections. But Senators McCain and Graham, who have steadfastly called for more troops, not fewer, voted against Mr. Warner's plan, saying it smacked of a timetable for withdrawal.
Yet the three are firm in their conviction that Congress, having ceded authority on military matters to the executive branch, must flex its muscles. In addition to sticking together on the so-called torture ban - despite a White House veto threat - they joined last week in backing a bipartisan compromise, sponsored by Senator Graham, giving "enemy combatants" in Guantαnamo Bay, Cuba, limited rights of appeal in federal court.
"This was a huge 'Congress getting into the ballgame' week," Mr. Graham said. Mr. Warner said wryly, "You know, Congress is a co-equal branch."
But Congress is hardly united, and now the three senators must contend with House Republicans. On Thursday, Mr. Warner met with his House counterpart, Representative Duncan Hunter of California, to discuss the military spending bill, which lacks the torture provision in the House version.
Mr. Hunter said afterward that each man promised to give the other "a fair hearing." But Mr. Warner said he made his position clear.
"I told him as an opening salvo, 'I'm solid with John McCain,' " Mr. Warner said.
All three senators are also in the "Gang of 14," a bipartisan group that struck a deal on President Bush's judicial nominees. They trace their alliance on military matters to last year's revelations of detainee abuse at the Abu Ghraib prison in Iraq.
The scandal prompted Senator Warner, the committee chairman, to conduct hearings, over the objections of some Republicans who said he was handing a political issue to Democrats.
Mr. Graham says he became convinced at that time that Congress needed "a holistic approach" to the delicate issues surrounding those in American government custody. So he asked the committee chairman for permission to hold hearings on the legal rights of detainees. He recounts Mr. Warner's reply:
"He said: 'Go to it, young man.' "
Mr. McCain says he pressed for the torture provision because "frankly, we never got answers to some of the questions that were asked" about Abu Ghraib. The measure would require all American troops to use only interrogation techniques authorized in a new Army manual; the White House is now pressing to make clandestine Central Intelligence Agency activities exempt. Mr. McCain said last week that he was "hopeful, but not confident" the negotiations could produce a compromise.
"I think I can help the administration by forcing this through," he said. "I think I can help them more effectively pursue the war on terror in general and the war in Iraq in particular."
Not everyone in the Capitol is so convinced, and Mr. Graham says the three have "withstood a lot of pressure." The McCain provision received only nine "no" votes in the Senate, but four were from Republicans on the Armed Services Committee - a tally that suggests a possible rift within the panel. One of the four, Senator John Cornyn of Texas, complained last week that his colleagues had given Democrats an opening to politicize the Iraq war.
"I think McCain galvanized opinion on this issue because of who he is and what he's been through," Mr. Cornyn said, "in a way that probably no one else could."
For Democrats, who have spent months trying to put the public spotlight on the issues of detainee treatment and the war in Iraq, the three Republicans are like some kind of gift from the political gods. After the Senate overwhelmingly adopted Mr. Warner's measure on the war, Senator Joseph R. Biden Jr., Democrat of Delaware, stood slack-jawed.
"It's gigantic," Mr. Biden said.
Perhaps that is because Mr. Warner, who characterizes his own military service as "very modest," has such strong defense bona fides: He has been associated with the armed services, in one form or another, for 60 years. But Mr. Biden said military ties are not the main reason Senators Warner, McCain and Graham have such strong credibility.
"I think their credibility," Mr. Biden said, "is mainly, they're Republicans."
