The question they will answer in conference is which, if any, of the cases they will hear oral arguments on. They could deny cert and let the lower courts' decisions to stand without comment, they could decide to hear each of the individual cases, combing those asking the same basic constitutional question or they could remand to the lower courts with or for clarification.
After talking to a friend who has experience with the Supreme Court and considering the ideologies of the individual justices, I believe the following decisions will be made:
- Prop 8 and Arizona - Both cases basically come down to can a right that was recognized be taken away. In both cases, the 9th Circuit ruled that no, you can't take a way a right previously recognized. I think the Supreme Court is going to deny cert in both cases. As much as certain justices might be biting at the bit to rule one way or the other, I believe that they don't want to delve into this issue just yet. By denying the cert, they don't have to rule on the broader issues and the decisions of the lower courts are narrow enough for the Justices to feel comfortable in denying cert.
- DOMA - I think the Justices will agree to hear the cases, but in a combined format. I also think that the Justices will punt by deciding which standard of scrutiny the various courts are supposed to use in regards to marriage equality without dealing with whether or not DOMA is constitutional.
Lyle Denniston over at SCOTUSBlog is doing a great preview of the cases. Be sure to check it out for more views.