My dad has been a meat cutter for 50 years this year. He just retired this past July and did it with 10 finger nails!!!!!!!!! Thats a very big accomplishment for someone been in the business that long!!! I know he has dealt with over 20K deer in his time!!!!
I will say from him doing it that time, it can and does take up to 2 weeks to get it taken care of. Skinning, de-boneing, grinding, mixing in the spices, re-grinding, stuffing or smoking. It all takes time, depending on what you wanted to have done. Especially if he had other deer to do in addition to yours and that does not take into consideration to any that were brought in after yours or if he had any to do before yours.
Point being, you got your deer, got it to the processor, now sit back and give it a minute, perfection takes time!!! Would you rather have him hurry and mess up your order or would you rather have him take care of it correctly? Who knows, something may have came up in between and he was delayed for a minute.
Give him till the middle/end of next week and see what comes up.