You also have to be honest about the number. If you say you will sign for $1 million and then panic and sign for $400k in the 8th round, you've lied to the scouts (who don't really care), your college coach who accepted your commitment (this matters some), and most importantly, yourself. Because in a year (at most) you will be wondering if you should have held out.
The reality is that a hell of a lot changes when that check is placed in front of you for $500k when you wanted $800k. Are you going to walk away from that kind of money? Not many 18 year olds have the fortitude to do so.