They can push you to do better once you're there but you should push yourself to get into shape now like you're doing. Eat more greens, healthier food will fill you up and give you more energy. Run 30/60s and 60/120s (sprint for 30/60 seconds and walk for 60/120 seconds) since what it seems like is you burn out before a real excersize has started. If thats not the case and you're holding your breath then think about breathing the entire time you're running and breathe every 2-3 steps.
As far as pushups go you can get some low weight dumbbells and lay on your back and do a bench press sort of deal to help but other than that just doing more pushups will increase your numbers. Do as many as you can in one day, take the next day off and then do 1-5 more than you previously did the next day (write your numbers down). If you push yourself and workout 4 days a week you'll get there. You'll be fine if you truely want to join, just work on what you can now and make sure to push yourself once you're there.