It's really a pretty short document that anyone can read in a few minutes. Bill Clinton would be prohibited from running on the VP ticket in part because the 12th Amendment states that "But no person constitutionally ineligible to the office of President shall be eligible to that of Vice-President of the United States."

How is Bill Clinton ineligible to be President again? Well, the 22nd Amendment states that "No person shall be elected to the office of the President more than twice, and no person who has held the office of President, or acted as President, for more than two years of a term to which some other person was elected President shall be elected to the office of the President more than once."

In simple terms, since BC is prohibited by the 22nd Amendment from being President again, he's also prohibited from running for Vice President.

The 22nd Amendment is part of the Constitution, so how can it be unconstitutional? It was properly passed by a 2/3rds majority of both houses of Congress and ratified by the states. You might as well say that anything else in the Constitution is unconstitutional if you don't like it.

Now, if they're really serious about it, they can propose a new amendment to cancel out the 22nd Amendment, like what happened when the 21st Amendment overturned the 18th Amendment. All it would take is to get the amendment legislation passed by a 2/3rds majority in both houses of Congress and ratified by 38 states. I'm not holding my breath on that one.