If the Constitution's requirements have not been met, then yes. Judges do that all the time. At all levels. See Bush vs. Gore in Florida.
The Constitution doesn’t give the courts the right to rule on Obama’s eligibility. That role is given to Congress.
If the Constitution's requirements have not been met, then yes. Judges do that all the time. At all levels. See Bush vs. Gore in Florida.
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Since we are (or, supposed to be) a Constitutional republic and NOT a "democracy", yes. It's thanks to this republic that "minorities" (of any kind) have a voice and have protections under the Constitution.
If the masses (i.e. majority) vote someone into office that isn't Constitutionally eligible, then they should be found ineligibly by the judiciary. From there, how they are removed (if they don't leave on their own free will) is up to law enforcement.