I've used a 308 for several elk kills. All were basically short range in timber. Depending on the situation, a 308 could be fine. As already stated you will need to discipline yourself to reasonable ranges.

If the hunt is a one time deal and you shoot the gun well I would use it. If you're looking for a long-term go-to elk gun you might look at another weapon. Especially if you are hunting open country where that far away bull will be awfully tempting. If that is the situation you'd be better off looking for something else now. My two cents.