Would a court block Cruz from the presidency?

I argue in Slate that Cruz is ineligible for the presidency. But would a court stop him if someone sued?

Courts employ various devices to avoid deciding uncomfortable, politically charged questions. For example, the political question doctrine deprives courts of jurisdiction over issues that are inherently “political,” meaning that the Constitution grants jurisdiction to other parts of the government to decide the issue, or the issue just is not amenable to judicial evaluation because it requires a “policy” judgment rather than a “legal” judgment. A prominent example is impeachment: if the president is impeached and convicted, a court won’t second-guess the Senate. However, the eligibility rules are different. Imagine that Miley Cyrus is elected president. The Constitution sets the minimum age at 35; would a court block 23-year-old Miley from office? Imaginably, yes. There’s nothing difficult about determining someone’s age or what the constitutional provision means. What if the person is not a “natural born citizen”? Justin Bieber, 14 years hence. Also, imaginably, yes. If so, and if Cruz is found not be a natural born citizen, then yes for Cruz as well?

In 2008, a person named Markham Robinson brought a lawsuit arguing that John McCain could not occupy the White House because McCain was born on a naval base in the Panama Canal Zone. The court dismissed the suit because Robinson—who wanted to become an elector for long-shot candidate Alan Keyes—could not show that he was injured by McCain’s candidacy—and must in any event wait until after the election to bring his lawsuit since the Constitution charges Congress in the first instance with the task of evaluating election results. It’s also not clear that Hillary Clinton or Bernie Sanders could challenge Cruz if he won the election, since the remedy—Cruz stepping down—would give the presidency to his vice-president rather than to Clinton or Sanders. Clinton/Sanders, like Robinson, would not have suffered an injury. However, Cruz might want to choose his vice-president very carefully.