I take that back, the passport shows place of birth, and so is sufficient.
Of course you have to submit a birth certificate to get a passport, or other official documentation of place of birth such as: (From state department website):
Previously issued, undamaged U.S. Passport
Certified birth certificate issued by the city, county or state*
check box Consular Report of Birth Abroad or Certification of Birth Naturalization Certificate
Certificate of Citizenship
*A certified birth certificate has a registrar's raised, embossed, impressed or multicolored seal, registrar’s signature, and the date the certificate was filed with the registrar's office, which must be within 1 year of your birth. Please note, some short (abstract) versions of birth certificates may not be acceptable for passport purposes.
A quick search did not reveal which short form BC's were and which were not acceptable, except that California's and Texas' are not.
Bruce Fein said that any State Secretary of State could demand a birth certificate of the candidates in order to insure that the candidate had the necessary qualifications to appear on the State ballot. I don’t know if there are any agressive Secretaries of State out there or not. That could be a path to take for clarification of Obama’s birth certificate.