Thanks to analysis by EPPC's Ed Whelan, it is possible that the time the Prop 8 same-sex marriage proponents had to file their Motion to Vacate Stay was even less than FRC stated in its Freedom of Information Act request to DoJ. Here is what Whelan writes in a post on NROs "Bench Memos" webpage:

Specifically: From what I can tell (and I invite correction on the point), the text of Attorney General Holders letter announcing the Obama administrations decision to abandon the defense of DOMA apparently became publicly available somewhere around 12:30 p.m. Eastern time last Wednesday. Prop 8 plaintiffs filed their motion (according to the electronic notice issued by the Ninth Circuit) at 9:56 a.m. Pacific timei.e., 12:56 p.m. Eastern time. And somehow Prop 8 plaintiffs were able to quote from Holders letter in their motion and include a copy of the letter as an attachment to their motion.

Of particular interest to me is the fact that the Motion was filed before 1:00 p.m. EST. Under Whelans calculation this would have given them about a half-hour window for cutting, pasting, and filing.