This is a Petition for a Writ of Certiorari. The Petitioner has to be granted certiorari for the case either to proceed to a hearing before the SCOTUS or to go back to the Appeals court on remand. If certiorari is not granted, it’s not going anywhere.
That may be why the attacks on Thomas have started, they want to have him recuse himself from this one due to his wife voicing an opinion on the matter (or at least I'm told she has, I haven't found it myself. My guess is that they'll grant the writ due to the fact that everything is put together so well. Then, however, it'll have to go back down and worm all the way back up, something that will surely take more than two years. Since that's after the next election, the Court can either hear it after several states have demanded the BC before letting him on the 2012 ballot which would be solid grounds, or refuse to hear it because Barry is already out of office in which case a separate case would need to be built asking for a ruling on what constitutes a natural born citizen for reasons of being placed on a ballot.
JMHO
Regards