He will do anything to bring Obama down.
Alito could if he wanted to make Taitz go away. He didn't and he doesn't. He's got other plans which I fear are not good.
As it turns out, though, it's standard operating procedure for the second justice who receives an application to forward it to the full court. From the Supreme Court's official reporter's guide to applications (PDF):
If a Justice acts alone to deny an application, a petitioner may renew the application to any other Justice of his or her choice, and theoretically can continue until a majority of the Court has denied the application. In practice, renewed applications usually are referred to the full Court to avoid such a prolonged procedure.
So there you go. Taitz had vowed to apply to each justice. Apparently it's been tried before, and the court has come up with a way of dealing with it.
"The Justices have a policy of referring these second requests to the full Court so that applicants don't succeed in cherry-picking who will hear their stay requests," Tom Goldstein, a lawyer and publisher of SCOTUSblog, told TPMmuckraker.
Now, in order for Taitz's application to be approved, five justices must agree to it. It only takes four justices to grant cert -- that is, agree to hear an appeal of a lower court's decision -- but Taitz has not filed the much more formal writ of certiorari.