[jamese777]

Recussals by Sotomayor and Kagan (and no votes by Bader-Ginsberg and Breyer) are irrelevant to moving this appeal to a hearing before the full court.
It takes FOUR votes (the rule of four) to grant a Petition for a Writ of Certiorari, which is Supreme Courtese for “yes, we’ll hear your case.” There are five Justices appointed by Republican Presidents: Alito, Kennedy, Roberts, Scalia, and Thomas.
Sotomayor and Kagan are not needed.

[devattel]

This is the right observation for the acceptance of the case. However, they can influence the final decision should it be accepted.

If the rumor is correct with regards to the number of members who want to address this case, I am going to assume it is Alito, Scalia, and Thomas who are the ones who want to resolve the issue. Roberts would have to admit he suspected a problem when he swore Obama in and did nothing to address it. Kennedy is most likely sitting on the fence.