I got the # by seeing how many HV's it took at D1 to get the tight message. It was a while ago but I think it was 23 or 24. There may be other factors I didn't include like prestige, considering credit, and/or quality of the recruit.
I have tested it out in D2 by trying to take a recruit off SIM. It took 21 or 22.
I've gotten the *tight message* at d2 as well but it was always after a battle where the other guy filled his scholarships. It was less than 20 HV's but I figured it was considering credit.
It may be a little less but I am pretty confident the # is close to 23. It probably also varies a little bit for each recruit because of the components of recruiting that are minor (prestige, close to home, favorite school, recruit threshold).