Eligibility is not a political issue, is a question of law & fact. The facts regarding an individual are discoverable. For example, a persons age and residency are discoverable facts, as is their citizenship status. Questions regarding eligibility are within the exclusive authority of the Judiciary. Conversely, if it were a political issue, the eligibility mandate of Article II would be nugatory.
In the end, all constitutional questions are political questions, by virtue of the fact that the Constitution belongs to We the People, not to the judges or politicians.
Eligibility of a candidate can be challenged on a state by state basis, typically through the state’s board of elections. Cruz has already been challenged for ballot access in New Hampshire and the Secretary of State rejected that challenge. Their rejection of the challenge is instructive. They only cared that prima fascia eligibility was established. They didn’t want to deal with constitutional interpretation. They viewed that as someone else’s job.
And at the federal level, because alternate means exist to “adjudicate” the problem, and those means are part of the political structure, Congress, the electoral college, etc., federal courts are strongly inclined to treat presidential eligibility as a political question and pass that buck to anyone else they can find.
See here for further reading, if you are interested:
http://repository.law.umich.edu/cgi/viewcontent.cgi?article=1087&context=mlr_fi
Peace,
SR