You'll be fine. Animals have been gut shot for as long as we have been hunting them, and eating them.

Don't let the contents from the intestines soak into the meat, and you won't have any problems. Basically, gut your deer as soon as you can, and you lessen the likelihood of any potential problems.

I've eaten many deer that were gut shot over the years. The worst ones required us to forego the inside tenderloins, but the rest of the meat was fine.