Eligibility is not a political question, it is a legal question. Legal questions are decided judicially.
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).
“Eligibility is not a political question, it is a legal question. Legal questions are decided judicially.”
Why then do you suppose the founders, who were quite economical with words, spent so many of them instructing Congress exactly how the votes were to be counted?