There is NO demand in State or Federal law that ANYONE has to verify eligibility of a Presidential candidated. With new laws being passed in many States in 2011 this should become mandatory. Putting an end to Obama 2012 unless he can slip a PERFECT forgery by everyone.
Each of the states have their own requirements to appear on their respective ballots. Most require an affidavit or certification to be filed with the chief election officers of the state, usually the Sec. of State, certifying the candidate is the nominee is the party and is eligible for the office. Some states require the candidate sign the document, other states do not.
A proposal that is being floated about, and that I am strongly in favor of, is requiring each Presidential candidate to file a certified copy of his birth certificate with the state. The BC must the same as that accepted by the government to receive a passport. That simple law will address the question to the satisfaction of 99% of the population and is so reasonable that not even the dumbocrats can object to it.