If you're barely turning in your applications now at the deadline... I'd hate to say it and not trying to be a sour pus but there's a high probability that you've slimmed your chances tremendously. With the amount of applications schools get, your application may be placed at the bottom of the pile. And by that time, most schools may have filled up their classes for the entering class that year. That's why they recommend to apply as early as possible due to this case.
However, Good Luck to you! Wishing you the best! 😀