It can be done... but you'll have to feed like a feedlot does, not like the typical 4H kids do.
What's your minimum weight?
You're looking at needing to feed grain at 2-3% of his body weight, and grain will make up 85-92% of his diet. You'll want him on a grain with a coccidiostat like Rumensin to even out intake, and if possible Tylan to prevent liver abscesses. You'll probably be feeding hay or silage at 2-3 lbs per day. His feed schedule will need to be very strict to prevent bloat and acidosis - fluctuations in feed type and amount and time of arrival are really bad when they're on a hot ration. It'll take 3-4 weeks to get him up to full feed. You're probably not going to be finished at 144 days unless he has some serious compensatory gain he can make up (and he might, recovering from coccidiosis), but he can be 1100 lbs and have the fat cover to look finished to someone without feedlot experience.
Weigh your options, risks/benefits, and then make your decision - but don't wait too long!
ETA - how important is it for this calf to make weight? do your kids have a backup option? If you're really not a cattle person I'd be really reluctant to advise you to push the calf that hard. There's a lot of things that can go wrong with a calf.
Shucks I'd have a backup steer, just in case, if I were pushing a calf that fast.