Biden was wrong on the vice-president’s constitutional role as related to the senate:
In attacking Vice President Dick Cheney, Mr. Biden said the vice president’s only role is to support the president and to preside over the Senate “only in a time when in fact there’s a tie vote. The Constitution is explicit.”
The Constitution, though, actually says the vice president is always president of the Senate and legal scholars say he has the right to preside at any time. Early vice presidents, such as Thomas Jefferson, actively exercised that role, the vice president still keeps offices at the Capitol, and scholars say it wasn’t until the middle of the 20th century that the vice president had an office at the executive office building.