Biden had a strong reputation for working across the aisle with Republicans and has counted some of the most conservative members of the Senate as friends, exemplified by his speaking at the funeral service for South Carolina Republican Strom Thurmond.
Unlike Cheney, Biden will not sit in on the Democratic caucus' weekly luncheons because he does not see that as part of his role.
"He believes in the independence of the legislative branch," a White House official said. "He believes it was inappropriate for Cheney to impose himself like the father figure and tell them all how to vote and what to do."
As vice president, Biden is not likely to fly into war zones on fact-finding missions as he did in his Senate days. But he has indicated he intends to play a key role in foreign policy issues as Obama's top counselor.
Yet Biden's efforts could be complicated with the appointments of several heavyweights in top foreign policy positions, starting with Secretary of State Hillary Clinton. Clinton will lead the administration's diplomatic efforts and will be backed up on hot-button issues by two newly appointed envoys -- Richard Holbrooke, special representative to Afghanistan and Pakistan and George Mitchell, special representative to the Middle East.
Holbrooke and Mitchell bring extensive foreign policy experience to their new positions and will hold significant authority as the primary point person on those regions. Biden's challenge will be to craft a unique role for himself from his position in the West Wing, drawing on his own experience in those regions.
"I do think it complicates Biden's job, I don't think it makes it impossible but the idea that Biden would follow to some extent the Gore model of having a few specific issues of expertise is complicated by the appointments of Holbrooke and Mitchell," O'Hanlon said.
A White House official dismissed the notion that having such strong figures at the table on foreign policy would push Biden out.
"If the world were at peace, if after the election suddenly all of our international problems had been solved or reduced to minor irritants, we would have too much, too many qualified people in important positions. Would that were the case," a White House official said. "There's plenty to go around."
This week, Biden embarks on his first foreign trip as vice president when he travels to Germany to speak at the 45th Munich Conference on Security Policy, an annual gathering of government officials and foreign policy and defense policy experts.
Traditionally, the secretary of defense attends this conference, but instead Biden will lead a high-powered contingent from the Obama administration that includes the national security advisor, retired Gen. Jim Jones, and Holbrooke.
White House officials said this does not in any way diminish Biden's role on the trip but instead shows the U.S. wants to bring firepower to the conference and highlight a renewed commitment to working with European allies.
As for Biden's larger, more general role on foreign policy, he told ABC News' George Stephanopoulos that he was meeting separately with the Obama foreign policy team to come up with a "baseline" on the situation on the ground in Iraq, Afghanistan and Pakistan.
O'Hanlon noted that Biden also could craft a unique role on East Asia issues, particularly China, or focus on energy and climate change, given that there is no heavy hitter yet assigned to these issues.