I am the type of hunter who always likes a little more gun than the bare minimum, as it's better to have more HP and not need it, than to need it and not have it. I also like heavy for caliber bullets and large diameter bullets as well.
When I discovered and fell in love with shooting a rifle, I used a 3-06 for a while with 180gr Core-Lokt's, and then switched to a .243 for a short time. That .243 is the reason I am so adamant about large, heavy for caliber bullets and having enough HP to do the job and then some. I had a 160-170lb buck, can't remember for sure how big, run for hours after taking a 100gr Nosler Ballistic Tip through it's lungs and appear as though nothing had happened. It was the most miserable day I ever had hunting, and have always used plenty of gun ever since.
I also watched a friend of my father give his Remington 7400 in .243 several bat swings into a tree while holding the barrel, as he had hit 2 deer with it on separate occasions, and both needed to be tracked for a long time. He was simply fed up with it's inability to anchor the tough deer we have around here.
The reason I write this is not to discredit the 7-08, or even the .243. But simply to say that every round has it's limits, and some need specific shot placement on certain animals to be effective. A shot that will work with a 30-06 may not be enough with a .243, so you may need to use different shot placement. You don't need a ton of HP to put an animal down, but smaller rounds require much more precise shot placement to be effective most times, so you need to be much more careful to assure proper placement.
It's very possible to kill a bull elk with even a .223, but it will likely not go down nearly as fast as when hit with a larger round, and shot placement will be extremely critical. The 7-08 has the power necessary to make kills on large animals, such as elk. But due to it having less bullet weight and power than a larger round, you need to carefully choose your shots for them to be as effective as those from a larger round.
The 7-08 is truly a great round, and has the power necessary to kill most any animal you encounter. But, it needs very good shot placement to be as effective as say a 338 win mag or even a 35 whelen. It will still get the job done, you just need to be careful.
With that being said I know where Otter and Kenny474 are coming from, elk are massive and extremely tough animals. I totally agree with Kenny, I like to break them down in the front shoulders,then even if there not dead they don't go anywhere!!! and you can finnish them off,animal found,meat in the freezer! The 7mm-08 WILL NOT DO THIS WITH ANY BULLET COMBONATION PERIOD there is simply not enough horsepower!!with that being said shot placement @ a distance that the bullet will reliably expand is esential for a ethical 1 shot kill. There are signs all over our highway systems that say drink resposably,there need to be signs on our back roads that reads. 
I live in steep rugged and for the most part wide open country so sometimes shots are long, If they can keep there legs under them they can run a long ways and that is almost allways DOWN HILL @ the bottom it is often steep brushy and unacessable by vehicle's so stopping them up on top is a big big plus most of the time,hence taking the front end OUT!! Happy hunting to you as well my friend 
