The Circuit Justices do not apply uniform rules when it comes to emergency applications. Justice Jackson, for example, refused to promptly call for a response in Libby v. Fectau, a case where the majority ultimately granted emergency docket relief.
I have also been keeping my eye on Trump v. AFGE. On May 9, A federal district court issued a TRO against the Trump Administration to block the removal of certain employees. On May 16, the Solicitor General applied for an emergency stay with Circuit Justice Kagan. And Kagan did absolutely nothing. She didn’t even call for a reply.
On May 22, the District Court entered a preliminary injunction, which the government promptly appealed. On May 23, the Solicitor General filed a letter with the Supreme Court, withdrawing the stay application. The short letter states: