"Vice President Cheney's been the most dangerous vice president we've had, probably, in American history," Biden said.
Biden used Cheney as a frequent target on the campaign trail and declared that Bush's vice president had a "recklessly" expansive view of the powers of his office. He pledged to do things differently, which Cheney mocked as Biden weakening his own influence.
"If he wants to diminish the office of vice president, that's obviously his call," Cheney said in a television interview last December. "And apparently, from the way they're talking about it, he does not expect him to have as consequential a role as I've had during my time."
One thing Biden has in common with Cheney is that he is approaching the office with a lack of personal political ambition. If Obama were to win re-election in 2012, it is unlikely that Biden, at age 73, would run for president again in 2016.
"Lacking a personal political ambition to go further is one big factor in whether you have the confidence of the president. If the president is always wondering if you are trying to advance your candidacy for four or eight years from now, it undermines your relationship," said Barton Gellman, author of "Angler: The Cheney Vice Presidency." "Biden has the same advantage that Cheney had in that he has no personal political agenda. But Cheney showed that that is not at all the same thing as not having a policy agenda."
Both came into the position with decades of Washington experience behind them: Cheney's primarily on the White House end as a former chief of staff to President Gerald Ford and defense secretary under President George H.W. Bush.
During the early stages of the Bush presidency, Cheney was able to flex his muscle on foreign policy because he had no serious rival in the Cabinet, except for perhaps his close friend Defense Secretary Donald Rumsfeld. Biden comes into the position with those foreign policy heavyweights working on the same issues that he has spent considerable time focusing on in the Senate.
"Even if Biden were inclined to try and even if the president were to let him try, he's not likely to roll right over Clinton or Jim Jones or Bob Gates, because they know a lot and have been around," Gellman said.
What remains to be seen is how Biden will exert his authority in order to achieve a level of influence and power.
"Cheney had a will to power and knew exactly what he wanted and was intent on driving it through. Biden has lots of opinions and it's yet to be seen how strongly he feels about making his preferred policy choices happen," Gellman said.
White House officials say that Biden's influence will come in his role as adviser and expect that Biden will be there for all of the big decisions. These officials note that in the transition after Election Day, Obama sought out Biden's opinion on all key matters, including the selection of Cabinet members and key administration officials.
One risk for Biden if he chooses this approach, as an adviser with no specific policy portfolio, is that he could potentially be shut out when it is time to make decision on those issues. He will not have the time to devote himself to specific issues in a way that the members of the Cabinet or foreign policy envoys will be able to.
While trying to be an adviser on everything, he could wind up being a key influence on nothing.