5.56mm
No mandamus, but the DOJ won't ignore it.
When a party asks the Supreme Court to hear an appeal from a lower court, the other side is not required to respond, and very often doesn't-- the Court grants less than 1% of the requests to hear cases, so many parties save money by just ignoring the petition. But if the responding party doesn't file anything and the Court is thinking of granting the case, the Court will "invite" the responding party to file a late response. There is no requirement to do so [despite what the article says, this isn't technically an "order"], but everyone always does, because if they don't, the Court is likely to grant the petition.