Karen Ocamb at LGBT POV published a long Q&A with Jon Davidson of Lambda Legal earlier in the week attempting to sort out the possible routes should the Prop 8 case be appealed (if it even can be) and what might happen regarding Judge Walker's decision on the stay.

It's quite long, but here's a bit of it that might be helpful regarding Walker's decision today, which is scheduled to come down between 9 am and 12 pm PDT.

From LGBT POV (Q&A with Jon Davidson, Lambda Legal):

How will this get decided?

A definitive ruling on whether the proponents have a right to appeal if the defendants do not is not likely to be made in connection with the consideration of whether or not Judge Walker's order should be stayed pending appeal. Judge Walker or a higher court may comment on the issue, however, as part of deciding whether the proponents have shown they are likely to succeed on the appeal because, if the proponents have no right to appeal, they obviously can't show they likely would prevail on an appeal.
If the defendants do not appeal within the permitted time (30 days from the time Judge Walker's order is entered, which will be when he rules on the motion for a stay pending appeal), then the plaintiffs and San Francisco could file a motion to dismiss the appeal that has already been filed by the proponents on the ground that the proponents hah no right to appeal. In the alternative, the plaintiffs and San Francisco could raise the issue of the proponents' right to appeal or not as part of their briefing opposing the merits of the proponents' appeal.

If the three judges randomly assigned to hear the case at the Ninth Circuit dismiss the appeal, the proponents could ask the 27 judges on the Ninth Circuit to reconsider that. If a majority of those judges agree to do that, the question would be decided by a panel of 11 randomly assigned to hear the case “en banc” (which refers to a hearing by a large component of the appellate court). Whether they hear it or not, if the appeal is dismissed, the proponents could ask the Supreme Court to decide whether they have a right to appeal. If the Supreme Court declines to hear that, the case is over. If the Supreme Court agrees to consider the question, it could decide that the proponents have no right to appeal and, again, the case would be over. If the Supreme Court were to decide that the proponents do have a right to appeal, the Court likely would send the case back to the Ninth Circuit for three judges to initially decide the merits of the appeal, resulting in a delay of the final determination of the validity of Prop 8 for some time.
In other words, it could indeed be decided that, if the government defendants do not appeal, the proponents cannot and the case will be over. In that situation, same-sex couples will be permanently allowed to marry in California. Judge Walker's ruling will stand and it may have an impact on future cases dealing with the right of same-sex couples to marry, but it would not itself change the marriage laws of any state other than California.

So, bottom line, will Judge Walker grant the further stay or not?

In a recent decision, the Supreme Court explained that whether or not to issue a stay pending appeal depends upon the circumstances of a particular case. The Court has cautioned lower courts against “reflexively holding a final order in abeyance pending review.” In cases in which state trial courts have held that a state's ban on same-sex couples marrying violates the state's constitution, the parties either agreed to a stay or the courts granted a motion by the defendants for a stay pending appeal. What makes the Perry case quite different from any of those, however, is that the defendants are opposing rather than seeking the stay and the stay is only being sought by intervenors, who have not been ordered to do anything, may not be able to show any legally-recognized harm, and may not even have a right to appeal.

So, no one can say for sure. As he's done throughout the case, Judge Walker is likely to carefully consider the legal standards and apply them to this case, taking into account how the appellate courts are likely to rule when the question is before them.

What happens if Judge Walker denies the stay pending appeal?

Even if he denies the proponents' stay pending appeal, Judge Walker might extend his temporary stay for a brief period of time (a week or so) in order to give the proponents time to ask for a stay from the Ninth Circuit while there's a temporary stay in place. If he does not do that, the proponents are likely to file a request for an emergency stay from the appellate court.

The Ninth Circuit would then apply the same test as Judge Walker did in deciding whether or not to issue a stay of Judge Walker's order pending the appeal. If they deny a stay as well, the proponents could ask Supreme Court Justice Anthony Kennedy (who reviews such matters arising out of the Ninth Circuit) to issue a stay pending the appeal. If he also denies a stay, the proponents could seek a stay from the full Supreme Court.