After years of globe-trotting in Air Force Two attending funerals of world leaders, George H.W. Bush once joked that the best tools for the job were a black hat and veil.

Nobody would make that suggestion to Vice President Dick Cheney (search), even in jest.

On Thursday, he was walking among dozens of heads of state at Auschwitz (search), commemorating 60 years since the liberation of the Nazi death camp. On Wednesday, he met for more than an hour with the new president of Ukraine (search) and chatted with the president of Poland, a staunch ally in the war in Iraq.

No longer trying to help President Bush get re-elected, Cheney now has more time to represent the president overseas. He went to Afghanistan last month to attend the inauguration of Hamid Karzai, the first popularly elected president of the new democracy formed after U.S.-led forces toppled the Taliban.

As Bush's second term begins, Cheney is also likely to spend more time on Capitol Hill, quietly lobbying for votes on Social Security, taxes and legal reforms.

He's a heartbeat away from being leader of the free world, but Cheney doesn't want the job — not even in 2008. That, combined with his loyalty to Bush, gives Cheney his power.

Paul Light, an expert on the vice presidency, calls Cheney the "vice president on steroids." Former Sen. Alan Simpson, R-Wyo., describes Cheney as the "heat shield," taking the fire so Bush won't have to.

"He would take a bullet for the president," said Simpson, a friend of Cheney's for decades. "When they throw him in the hole, they'll have a big `L' on his gravestone for loyalty."

The White House is focusing significant energy early in the second term to move legislation on items like simplifying the tax code and partially privatizing Social Security. The lame duck syndrome that two-term presidents often catch midway through their second four years is one reason to try to get legislative traction now. Another is that Republican lawmakers need a slate of accomplishments on which to run their midterm campaigns.

Cheney's role as the president's most senior legislative adviser was evident when Bush announced last week that he's picked Candida Wolff as his new chief lobbyist and liaison to Capitol Hill. Wolff used to be Cheney's legislative affairs director.

Cheney is due back on U.S. soil Friday, just days before Bush makes his State of the Union address, rolling out the legislative agenda that his second-in-command is charged with helping push through Congress.

The emphasis on domestic matters, however, won't push foreign policy and national security matters off his desk. His friends say he'll probably watch election returns that will be coming in from Iraq on Sunday, his 64th birthday.

Cheney's hefty vice presidential portfolio is a far cry from the job former President George H.W. Bush once joked about with Walter Mondale's running mate Geraldine Ferraro. When she asked him what she should do if elected vice president, the elder Bush told her, "Buy yourself a black hat with a veil."

Light, a fellow at Brookings Institution, thinks Cheney's role will become more ceremonial and less influential during Chapter 2 of the Bush presidency. Bush has matured as a president and no longer needs to lean on Cheney's weighty resume, he said. Light also believes that work of the second term will pivot on the administration's ability to reach compromises on domestic issues and exert a softer hand on the foreign stage.

"I'm not sure muscle is the answer, and you would never describe Cheney as a consensus-builder," Light said.

His aides, however, insist Cheney is not heavy-handed and is quite capable of finesse.

Cheney is a very serious guy. He reads books on military history and then more briefing papers, steeping himself in the intricacies of policymaking.

The vice president's chats with lawmakers often are one-on-one, without staff members in the room. Cheney is known to sit through entire meetings without uttering a word and then, with a few sentences in his trademark low murmur, quickly sum up what's been said. A lot of his work is not easy to track, leading some people to label him the "stealth VP."

When he's amused, his lips curl and he cocks his head with a half smile. When he's angry, expletives follow. Ask Democratic Sen. Patrick Leahy about that. Back in June, Cheney cursed Leahy on the Senate floor and later said, "I felt better after I said it."

Simpson recalls calling Cheney back in June to see how he was holding up under the pressures of the campaign, when pundits were suggesting he had become a liability.

"How you doing, pal?" Simpson asked Cheney.

"Same old crap, Al," Cheney replied.