The decision to allow Biden to take on arguably the most important piece of legislation in the first term is a testimony to the VP's influence in the administration. It was Joe Biden who the president called upon to head the commission to create recommendations on how to tackle the national issue. His counsel to the president was key to influencing decisions and without his ability to work with republicans who knows how much legislation would have made it through congress.
Joe Biden makes a fool of himself frequently and shows why he should not be the vice president, however this is the intention of having him as VP, it makes light of Barrack Obamas failures. In comparison to Joe Biden, it is easy to think that President Obama is an excellent president, as Joe Biden is dismissed by the politically aware and taken seriously by those unaware. He plays a unique role in which he is both a leader, backing up Barrack Obama, and a buffoon not to be taken seriously. Joe Biden is only influential to those without political awareness.
Biden is a good politician and has used his voluminous experience to augment Obama and give meat to his goals and objectives.
However, no one will come close to wielding the amount of power in the VP slot as Dick Cheney did, if for no other reason than Bush being something akin to the "absent in Chief". There was an evident power vacuum, and Dick Cheney filled it.