When I got to boot camp my biggest problem was that I was trying to do my shit with good form.  They don't give a fuck about the quality as long as you break 90 degrees on your pushups and touch your elbows to your thighs on the situps.  So cheat with it, bounce your way up on the pushups and don't waste your energy going down slow with it, knock them out as quickly as you can.  Same with situps, hug your knees closer to your body so it's not as much of a stretch and slam your back down so that you don't waste your core on the down portion.  I'm not sure about the other branches but with Navy we just had to crank out about 50 of each depending on your age in 2 minutes or less, as soon as you were done you could quit out.  As far as the run goes, it's all mental, take your mind off the burning and keep pushing, it's a big payout for a very small amount of time and effort.