I believe Joe Biden should go. He should not be on the Democratic ticket in the fall.
Let me be clear that this is not about his position on gay marriage. I support gay marriage. I think President Obama should support gay marriage.
But, from the perspective of how the presidency should work, a vice president should never force the hand of a president on a sensitive, first-order issue by getting out ahead publicly. This is true whether the issue is foreign policy, defense policy, economic policy, or social policy.
Biden committed a governmental sin of the first order. In any organization where the leader can fire the second in command--whether a university, an NGO, a corporation--Biden would have been asked to leave, if not immediately then before too long. Taking a controversial position (however "inadvertent") outside the government, not inside, is a good reason not to renew Biden's lease at the VP's house at the Naval Observatory in Washington.
Having refused to defend the Defense of Marriage Act and having done a excellent job of bringing "Don't Ask, Don't Tell" to an end, the president, in a politically fraught year, had the right to decide when and how to announce his support for gay marriage--and not be forced to act by his vice president, looking weak and disorganized in the process. (The reporting thus far does not suggest a Machiavellian two-step, with Biden testing the waters having gained Obama's approval in advance.)