My hunting partner likes to say "it is what it is." This seems to be a good workable expression that applies to anything. In this case, I suggest you look upon your physical conditioning and say "it is what it is!" You can begin working out, but you can't change your basic physical conditioning much in 4 weeks. Do it anyway. BUt don't OVERdo it: you could injure yourself.
While you are hunting, bear in mind that you may need to hunt for 5 days or more. Don't kill yourself on day one, because you may have to hunt 4 more days. As you are walking, when you get out of breath stop and catch your breath. You probably can't walk 3 miles climbing 2000 feet to get to your hunting spot without stopping to rest. It is what it is.
Eat well. Your body will expend a lot of energy, so you need to shovel the energy in. Take snacks with you out hunting. I like granola and nuts and dried fruit mixed together (GORP). Candy bars work. Eat breakfast. Eat dinner. I say this because sometimes the altitude and fatigue take it out of you so much you don't WANT to eat. Resist that impulse and eat.
If your physical condition gets in the way on this hunt, just say to yourself "It is what it is." Next year, however, or the year after that, when you plan to take your next elk hunt, start getting in physical shape 6 months in advance. Get your weight down. Build muscle strength. Build endurance through cardio exercises. I'm assuming this is your first elk hunt or you would already know this.
Don't forget what some people say -- a bad day hunting beats a good day at work. The elk hunting grounds are beautiful. 20% of elk hunters in the Rocky Mountains kill an elk, on average. It is what it is.