The U.S. Supreme Court is officially one justice short today, and the Court has issued a new order assigning circuit justices to the various federal circuits. Chief Justice Roberts has taken on the Ninth Circuit, formerly assigned to Justice Kennedy (Ret.), on top of his D.C., Fourth, and Federal Circuit assignments.
The circuit justice alone typically decides on certain extension requests, and their strictness or laxity varies. The late Justice Scalia was the strictest.
Requests to stay a lower court decision are formally addressed to the circuit justice, although absent an emergency the circuit justice generally refers the application to the full court. Justice Thomas, assigned to the Eleventh Circuit, grants short-term, single-justice stays in capital cases more often than the others, to give the Court time to consider the petition without an execution clock ticking.

Any chance there will be an execution date out of CA anytime soon? It is now almost 2 years since the people voted for a speed up, but it is hard to see any change from far away.
The state court injunction against executions has been vacated.
The problematic three-drug protocol that was the cause of the federal court stays has been rescinded and replaced with the superior one-drug protocol.
The problem is that a federal district judge continues to stay executions despite the fact that no Glossip showing has been made against the present protocol. That is clear, gross error, yet our corrections department fails to appeal. Three district attorneys tried to intervene, and the same judge rebuffed their intervention motions. Now the denial of intervention has to be appealed.
Jerry Brown promised while running for office that he would enforce the death penalty despite his personal opposition. He is quietly breaking that promise by sins of omission. It's tough to enforce the law when your chief executive intentionally fails in his constitutional duty to see that the laws are faithfully executed.