But as Mr. Bush enters his second term, Cheney's role is in flux. His chief task in the first administration — mentoring a novice president with little foreign policy or legislative experience — has been accomplished. He remains dogged by heart disease and an FBI probe of a subsidiary of Halliburton, the company he once ran.
Indeed, some wonder whether Cheney, with no ambition to succeed his boss in the White House, will serve out his second term. And while he has redefined a job that traditionally involved attending ceremonial and campaign events or undertaking thankless policy assignments, there is speculation Cheney's influence is waning.
"He was so influential that it was almost insulting to call him a vice president," said Paul Light, professor of public service at New York University. "He was a mentor, chair of the kitchen Cabinet, legitimizer, Rasputin — you name it — all rolled into one. Those roles have been chipped away over time."
Still, Cheney is likely to remain the administration point man on several fronts.
As Mr. Bush turns in his second term to forging his presidency's legacy, he is expected to use Cheney to push his domestic agenda — overhauling Social Security and the tax code — in Congress, where Cheney served for 10 years as a Wyoming congressman and where he still enjoys strong influence among House conservatives.
"The clock is ticking on this administration, and what they really need is muscle on Capitol Hill to get the president's agenda approved," Light said.
With Republicans seeking to keep the White House in 2008, Cheney will likely be involved behind the scenes in promoting a candidate Mr. Bush can endorse as his successor. Cheney isn't interested in the job himself, which those close to the administration say only enhances the relationship between the two men.
"One of the great gifts Cheney bestows upon Bush is he doesn't have any aspirations of being president," said Mike Franc, vice president for government relations at the conservative Heritage Foundation. With Al Gore, President Clinton's vice president, Franc said, "There was always a background tension because Gore himself harbored the presidential aspiration."
Franc conceded that early in his first term Mr. Bush, 58, "was deferring quite a bit" to Cheney, 63. But he said the two men have "a great partnership" and trust that will only be "deeper and fuller" in their second term.
He dismissed speculation that the FBI investigation into whether a Halliburton subsidiary improperly received lucrative federal government contracts for work in Iraq without competitive bidding was a serious distraction that could put pressure on Cheney to step down or render him ineffective.
"There are about 1,000 people who really care about that — and half are the media and the others are liberal blocs," Franc said. "That issue does not resonate."
Similarly, it's not clear that Cheney's health problems could shorten his time in office. In 2001, he had an implantable defibrillator inserted in his chest. The device is designed to activate automatically if needed to regulate his heartbeat. Cheney also takes medication to lower his cholesterol and has said he is exercising and eating healthier.
John Nichols, author of the book, "Dick: The Man Who is President," said in an interview that Cheney may well "take a lesser role in the spotlight" as the political ambitions of GOP presidential aspirants emerge.
"Cheney is somewhat disempowered because there will be people moving to make a name within the administration and in the periphery of it," Nichols said. "He may even step back and allow someone else to have a definitional role."
But, he added, "My prediction is that Dick Cheney will remain in the second term the most powerful vice president in American history by quietly peopling" the administration "with folks he's familiar with and who are ideological and personal allies."
Cheney's power, and his seemingly coequal relationship with the man ostensibly his boss, troubles one former vice president — Democrat Walter Mondale, who held the job in President Carter's one-term administration.
"I moved into the White House and I became a part of the internal workings of the Carter administration," Mondale said in an interview. "That precedent has been sustained throughout all the later vice presidents, which has made the office more important."
But "Bush and Cheney have taken it a step beyond what we were thinking about," Mondale said. "I thought, and Carter thought, that I could be helpful to him in his presidency, but I wasn't there as a prime minister or as an assistant president. I was the vice president in a subordinate role."
Mondale said he found accounts of Cheney's powerful role "troubling" because it appeared that Cheney was "directly and operationally involved in central issues" in a way that put him between key government officials and the president, possibly inhibiting their advice to Mr. Bush.
"I would have considered it improper," Mondale said. "I was always afraid of intimidating other public officers by implying that I was representing the president. ... The vice president can really help the president, but I think he has to be careful of chilling the atmosphere."
With Cheney's first term as a pattern, Mondale added, "I can't believe he will operate differently this time."