Of course it is. And it really has nothing to do with Obama. The SCOTUS needs to get 4 justices to agree to take an appeal and tell us what a "natural born Citizen" is.
They might well rule against what you desire. Or for it. After that, it is up to Congress to use that ruling, or not use it against Obama. What the SCOTUS doing its job would mean is the clarification of the issue for future candidates.
One might well accuse Congress of neglecting it's duty. However, they are just like us in that there are differing opinions on what that duty might be in this case. That's why we have a SCOTUS, to tell us what the COTUS means.
It's a "Failure to qualify" issue under the Twentieth Amendment, Section Three. If there is no valid birth certificate upon which to prove eligibility, Congress has allowed a usurpation to occur by FAILING to enforce this amendment.
Where does it say it has to be a Birth Certificate. What is the "proof of eligibility." the 20th is an Amendment ... a part of the COTUS. When there's a problem, it is the SCOTUS' constitutional duty to accept appeals that define the meaning of the Constitution.
Please note again that the courts cannot remove the President. Just as the Congress cannot ultimately define the Constitution.
I am not defending the pusillanimity of Congress in this matter, just that the SCOTUS' is more egregious.
This isn't necessary as it's been settled by Minor vs Happersatt. In addition, the "natural born citizen" question is a red herring.
The President Elect is tasked with "failing or not failing to qualify" under the Twentieth Amendment, Section Three. A failure to qualify forces Congress to act in naming a replacement. In order to act, they must be made aware of whether or not they have to act. If they didn't enforce the Twentieth Amendment, Section Three, this means that there has been a failure to qualify regardless of whether it's because there was no proof of eligibility given or they didn't act upon this non-proof. Both scenarios result in a usurpation of the office of President.
Even someone who is a natural born citizen will fail to qualify without being able to back it up with evidence to Congress. This is why the "natural born citizen" arguments are a waste of time. What should be discussed, and answered by our congressmen and women is how did they satisfy the demands of the Twentieth Amendment, Section Three. If they are unable to answer, they didn't. So far, I don't think any one of them has.