Really there isn't a "deadline" per se, at least for a 4 year Army ROTC national scholarship.
Just be mindful that until you pass DoDMERB, and pass the APFT, no monies will be disbursed to the college. So it is clearly in your best financial interest to get both of these things done quickly!
Many national AROTC award winners have already passed DoDMERB due to also applying to the Service Academies. That DoDMERB trasnfers over to AROTC. Once you select your college and accept your scholarship, the ROO should be opening your DoDMERB file.
Stay in touch with your ROO!