A review of the Second Circuit rules relating to motions allows the presiding judge of the panel great flexibility in scheduling oral arguments on motions. The following is a summary I took from a NY site on practice before the Second Circuit.
As to emergency motions, the presiding judge of the panel then sitting schedules emergency motions seeking a stay, and other motions presenting emergency circumstances. The motion is initially received and docketed by the Case Manager, who sends it to the Motion Attorneys. The Motion Attorneys contact counsel to determine whether the parties will maintain status quo until the motion may be calendared by non-emergency procedures; if not, the motion is sent immediately to the presiding judge.
The judge may set the motion for hearing by (a) that week's panel, (b) the following week's panel, (c) a subsequent panel, or (d) the first panel sitting after a bench memo is prepared. If immediate action is required, the judge may act as an emergency applications judge and provide an interim ruling (e.g., a temporary stay) pending full panel consideration. The judge may also determine that a bench memo is needed. If so, the motion and hearing date are promptly transmitted to the staff attorneys. If immediate consideration is required, the judge will normally set a hearing date that allows two days to prepare the bench memo; if not, (e.g., when a temporary stay was entered), the hearing date is set to allow at least one week for preparing the bench memo.