It's a constitutional question (not saying that isn't a form of legal question), and SCOTUS has been known to punt constitutional issues as being outside of judicial purview.
Eligibility of Obama would be a real hot potato, and SCOTUS would not want to be in the position of "decider" after getting booed by the glitterati for its Bush v. Gore decision. All it has to do is point to the part of the constitution that implies Congress decides issues of eligibility (20th Amendment).
The 20th Amend. says no such thing!
It specifies succession in the event of death(s) or failure(s) to qualify, and in the event neither President or Vice-President are qualified and alive then Congress shall "[declare] who shall then act as President, or the manner in which one who is to act shall be selected, and such person shall act accordingly until a President or Vice President shall have qualified." (emphasis added)
Congress does not decide eligibility but either declares, or provides a manner to select, who shall temporarily act as President.