Hi,
GMAC usually delivers official score reports to the selected schools within 48 hrs or sometimes even sooner than that. I would say you are really cutting it close but it may just about be enough to meet the Jan 10 deadline. Also, with Jan 7 being so close to a weekend, not sure how it will impact score delivery.
People usually reschedule their exam as the day gets closer so I would say login and check multiple times during the day to see if an earlier date has opened up - even a day or two earlier will likely be enough