When Vice President Dick Cheney addressed Senate Republicans last summer, a major Medicare bill hung in the balance.

Cheney often sits quietly at the GOP’s weekly policy lunches and listens to his colleagues, rarely divulging the administration’s position or delivering rousing speeches. During most of President Bush’s time in office, Cheney’s remarks carried enormous weight with his Republican colleagues.

Cheney, regarded as the most powerful vice president in history, has seen his influence wane over the last two years, according to interviews with more than two dozen senators. A politician who stays behind the scenes, Cheney speaks out only on select topics, and he keeps his views held closely to the vest. When he has exerted his power, he usually attracts GOP support — but his rhetoric has infuriated Democrats.

Sen. Bob Corker (R-Tenn.) says Cheney is the “lowest-key” person to attend the weekly policy lunches, even though he is the highest-ranking.

It remains to be seen what kind of role Vice President-elect Joe Biden, who was elected to the Senate in 1972 and has friends on both sides of the aisle, will play on Capitol Hill over the next four years. Biden has said he would pull back from Cheney’s expansive role.

Beyond his largely ceremonial role in the upper chamber, Cheney has found a regular presence on Capitol Hill, with constant efforts to reach out to Republicans, lunches with the Senate GOP and a leading role in pushing through big-ticket items, including the Patriot Act, the Iraq war authorizing resolution and energy legislation.

As president of the Senate, Cheney has broken eight tie votes, presiding over narrowly divided chambers in four Congresses. Al Gore, by comparison, broke four ties in his eight years as vice president under President Clinton.

Before the 20th century, vice presidents spent “99 percent” of their time in the Senate, according to Senate historian Don Ritchie. But after World War II, vice presidents typically took a much larger role in the executive branch, given special tasks to carry out the president’s mission.

By many accounts, Cheney has an enormous presence in both branches — and at one time declared himself part of neither, opening himself to ridicule by late-night comics.

He doesn’t have to schmooze with Republicans; his stature speaks for itself. “People come sit by him,” Sen. Thad Cochran (R-Miss.) said about Cheney’s dining mates during the Tuesday lunches.

Some see his eagerness to listen as a valuable resource to understand the GOP’s concerns and communicate them to the president, but others say failing to detail his views has hurt the administration.

“I think that he lost a lot of opportunity to give the administration’s points of view because not too often did he speak,” said Sen. Chuck Grassley of Iowa, ranking Republican on the Finance Committee.

Democrats generally have a nonexistent relationship with Cheney, who has most viciously sparred with the party over the Iraq war. In the last two years, after Democrats won back control of Congress, Cheney has largely taken a back seat on Capitol Hill, as his popularity ratings — along with the president’s — have plummeted.

“I have had virtually no contact with him,” said Sen. Kent Conrad (D-N.D.), Budget Committee chairman. “He doesn’t seem to be interested in it.”

“He’s colder, more aloof” than previous vice presidents, said Sen. Carl Levin (D-Mich.), chairman of the Armed Services Committee.

Lea Anne Foster, a spokeswoman for Cheney, said the vice president has “thoroughly enjoyed” his work with Congress on Bush’s agenda.

“He has a great deal of respect for the senators and appreciates the work they’ve done for the American people,” Foster said.

Cheney, in remarks during a 2007 question-and-answer session in his home state of Wyoming, said he had a “lot of friends who are liberal Democrats.”

“If you’re going to have an impact on events, if you’re going to persuade others that your point of view is the correct one, you’ve got to know what you believe,” Cheney, a former House minority whip, said.

He joked that his relationship with Senate Majority Leader Harry Reid (D-Nev.) is “better than my relationship with Pat Leahy,” referring to an infamous 2004 episode in which he told the Vermont Democratic senator during a photo-op to “Go f—k yourself” over a previous spat the two men had.

Asked about his relationship with Cheney now, Leahy said, “I love him.” He later clarified: “That’s a joke.”

At times, his testy relationship with Senate Democrats has carried over to the House, including a sparring match with Ways and Means Committee Chairman Charles Rangel (N.Y.), who evicted Cheney from his House office; Cheney had been the first vice president ever to set up shop in the lower chamber.

Reid and Cheney both say they have a pleasant personal relationship, but at times the two men have taken personal shots at one another, including in one of Cheney’s rare comments to the press after a Tuesday policy lunch.

In the heat of the Iraq debate in the spring of 2007, Cheney issued a stinging attack on Reid for advocating a withdrawal of troops from Iraq and saying the war had been “lost.”

“What’s most troubling about Sen. Reid’s comments yesterday is his defeatism,” Cheney said. “And the timetable legislation that he is now pursuing would guarantee defeat. Maybe it is a political calculation.”

Reid lashed back, in rather personal terms.

“The president sends out his attack dog often — that’s also known as Dick Cheney,” Reid said.

In a brief interview, Reid said the two men rarely agree, despite having a cordial relationship.

“I’m trying to think of something I agree with; I haven’t found it yet,” Reid said, adding that his conversations with Cheney are rare.

Some Democrats, like Sens. Mark Pryor (D-Ark.) and Ben Nelson (D-Neb.), say they have a friendly relationship with Cheney, but acknowledge they have little contact with the vice president.

“He doesn’t come out publicly very often and talk about what he’s doing,” Pryor said. “So it’s a little mysterious what role he actually plays.”

The role on Capitol Hill, Republicans say, was that of a critical earpiece for GOP concerns.

“We always recognized him as one of us, as president of the Senate, which is the first time that I’ve ever seen a vice president here utilize that effectively,” said Sen. Larry Craig (R-Idaho), who will retire at year’s end after serving 28 years in Congress.