According to the Federal Rules of Civil Procedure, there doesn't appear to be a time limit: Rule 8. Stay or Injunction Pending Appeal
Under Rule 8, "[a] party must ordinarily move first in the district court", unless "impracticible" (clearly not so in this case). Having made the motion, if "the district court denied the motion or failed to afford the relief requested", they can appeal to an appellate panel, but there are built-in due process requirements there (notice, etc).
So in theory the judge could delay a ruling on the motion for as long as he'd like, but at a certain point it would be likely that the 9th Circus would take it up under the auspices of the judge "fail[ing] to provide the relief requested". My guess would be the 9th wouldn't take it up for at least a few weeks if the DC chooses to delay.
Under Rule 8, "[a] party must ordinarily move first in the district court", unless "impracticible" (clearly not so in this case). Having made the motion, if "the district court denied the motion or failed to afford the relief requested", they can appeal to an appellate panel, but there are built-in due process requirements there (notice, etc).
So in theory the judge could delay a ruling on the motion for as long as he'd like, but at a certain point it would be likely that the 9th Circus would take it up under the auspices of the judge "fail[ing] to provide the relief requested". My guess would be the 9th wouldn't take it up for at least a few weeks if the DC chooses to delay.