That's incorrect. A Writ of Certiorari is an order from a superior court to an inferior (subordinate) court, demanding that the lower court transfer the case to the higher court. Asking for a Writ of Cert (petitioning for the writ) is asking the higher court to take the case. Berg has asked SCOTUS to take the case away from a lower court.
The mechanism for asking an appellate court to "take the case," where the appeal is not available as a matter of right, is a petition -- a request, if you will. Opponents to the request may file counterarguments, if they want to. But they aren't obliged to. The only thing due on Dec. 1 is a rebuttal to the petition for SCOTUS to take the case. There is absolutely no requirement that Obama present a birth certificate, or even a counter-argument.
IF CERT is not issued the case will not be heard.