My guess is the petition for a writ of certiori will be denied. The petitioner lacks standing. I also believe that it is not a justiciable matter. It is a political question. Only the Congress "qualifies" someone to be president. It is the first order of business when the new Congress convenes in January.
The case also fails on account of ripeness. Barack Obama was not elected president on November 4th. Only electors were chosen on November 4th. And the electors have not yet selected the next president. They convene in 51 separate "colleges" next month to cast their ballots. We won't know "oficial" results until January when the new Congress convenes in joint session and receives the electoral college certificates. At that point it takes the objection of at least one Senator and one member of the House of Representatives for the Congress to bring the matter to debate. The vote of the Congress is final. There is no role for the Supreme Court to intervene.(Just as the Supreme Court could not review a impeachment.)
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.