I sleep 5.5 to 6 hours a night, but I have always slept that much and would be sleeping that much even if I wasn't a resident. I would say that it is hard to guarantee more than 7 hours of sleep, but for the most part, except when on call (most places, every other weekend or once a month), it isn't hard to get that 7 hours if you need it. My typical schedule is as follows:
4:00 Wake-up, brush teeth, eat a yogurt, play with the cats for 2-3 minutes
4:15 Start running to hospital (~2 miles)
4:30 Shower
4:45 Meet with night float team to find out who they admitted overnight or what issues there were
5:00 Chart check all the patients on service (25-40 patients), update the list, identify issues that need to be dealt with and prepare for rounds
6:00 Round with the fellow
7:00 Run through the team list with the nurse practitioner
7:30 - 5:00 Cover the floors, morning is mostly discharges and dealing with overnight things, afternoon is mostly consults and ER patients. If things are slow and the NP has everything under control, I'll slip into the OR. We typically have 5-6 ORs running, so it is always easy to find someone who can use extra hands.
5:00 sign out the service pager to the night team
7:00 leave the hospital (between 5 and 7 finish seeing consults, taking care of post op patients etc)
7-10 - me time, I rock climb twice a week, but for the most part those hours are reading for cases the next day, research, preparing presentations etc.
You have the hours to sleep. I burn ~30 minutes every day running to the hospital and needing to shower at the hospital. I choose to climb a couple times a week. I also make sure that I read at least a little bit every day. The question is what your priorities are outside of the hospital.