What's a .243 Good For
I agree with the comments made by those that mentioned shooter experience, ethics, and bullet type.
In the past I have hit Elk between the shoulder blades with a Hornady 30-06 150gr SST Superformance that went down and then got back up, whereas with a Hornady Custom .243 100gr BTSP Interlock, same placement, they dropped like a rock, every time. Ranges where from 50 to 200yrds. (Locations with cwd I would avoid shots near spinal areas) Yes these shot placements lose some meat but for me are worth it for a quick kill.
The point is a well placed shot with a bonded round should work (and have) on any north american mammal using a .243 at short ranges, but think a bigger bore might be the wiser choice.