Why was the brief directed to Justice Anthony M. Kennedy?
Technically, the LCR asked Justice Kennedy to vacate the Ninth Circuit's stay. Each justice is given responsibility to deal with applications like this one and emergency motions and appeals over a particular circuit. Justice Ginsburg, for example, supervises the Second Circuit; Justice Kagan gets to oversee emergency appeals from the Sixth and Seventh Circuits; and so on. Justice Kennedy could decide this matter on his own, or he could refer the LCR's application to the entire Supreme Court. He has complete discretion here.
What happens next?
Justice Kennedy could rule on the application tomorrow, next week, next month or whenever. He could also request that the government file a brief in response, giving them a chance to get their voices heard. Again, Justice Kennedy has complete discretion here. It's good to be a Supreme Court justice!
If the stay is vacated…
then the military will once again have to start accepting openly gay and lesbian individuals into the service and would not be able to enforce the law against any service member currently in the armed forces. The appeal about whether DADT is unconstitutional would still go on, but it would go on while openly gay service members are free to serve.
If the stay is upheld…
then, DADT can still be enforced — albeit under the restrictions recently imposed by the administration — while the appeal goes on up the system.
If you have any other questions, let me know!
Here's the application itself: