I wouldn’t be surprised if the DC Cir. issues some form of opinion by mid-November. It’s even possible they affirm from the bench with opinion to follow. Then the DOJ would need to request an emergency stay from the Supreme Court. I believe that would require 5 votes. (“The Supreme Court has its own set of rules. According to these rules, four of the nine Justices must vote to accept a case. Five of the nine Justices must vote in order to grant a stay, e.g., a stay of execution in a death penalty case.”)
So, it’s not unlikely that the DC Cir. affirms the district court around mid-Nov. Then, then the DOJ seeks a stay in the SCt, which will likely reject the application for a stay within a week. So it’s probably over by Thanksgiving.
But, if the SCt does grant a stay, no way briefing is done and a decision issued until Mid-Feb or early March. That’s likely past the date for an impeachment trial in the Senate, and it would make things weird.