You could also reason that the electoral college in specific and the voting public in general, was defrauded by Obama as he represented himself as a eligible candidate(if the facts show he is not). At which time, allowing the electoral college to continue to operate under a known and perpetrated fraud would require relief.
I say it all depends on how much heat the Supreme Court is willing to take.
What relief could the Supreme Court grant? The Constitution does not provide for a new election. Do you want an activist court to take over the selection and qualification process? The Supreme Court is not going to get involved in this case, as I opined above. The Congress is empowered by the 12th Amendment to make the final decision. Any concerns should be addressed in a petition to the next Congress not to the courts.