As others have pointed out to you, it is Obama's responsibility to prove his qualification. Here's why:
The 20th Amendment says, "if the President elect shall have failed to qualify". See, the burden is placed on the President elect to qualify, not on others to disqualify him/her.
Also, as has been pointed out many times in the past few weeks, he will not be President elect until Dec 15th after the Electoral College votes. I'm thinking the USSC cannot require him to prove his qualifications until he is President elect.
That's a very good point, and one worth considering over the next two weeks.