If your talking a field dressed deer with the hide on you would have problems trying to keep that much surface and internal area sufficiently cold for a week just using ice.
If your are talking a deer that has been skinned, rinsed, and quartered, broken into primals, or boned you should be ok as long as the meat is bagged and is not sitting directly in the water from the ice melting. Drain the water daily and add more ice as needed and you should be good for the week.
As a precaution bring along a digital thermometer (around $10) and probe the hindquarters to make sure the internal temperature stays under 40 degrees throughout the week. The closer to 32 the better.
Good luck.
Dave