Remember though, for a team, getting a quality player that is under contract for 4-5-6 years at the price of the 10 year vet minimum (roughly) can be a boon for a franchise.
It very well might be considered the NFL's version of trading for a high 2nd rounder in the NBA (like for Euro's) so you can offer them whatever you want. (in other words high 2nd rounders in both leagues tend to be worth MORE than the picks just above them...in the NBA it's a guaranteed contract, I believe another year on the contract, and again the pick isn't slotted on the rookie scale so you can pay euro prospect enough to come over)
For the nfl any player you can lock up for 1-3 million a season for the duration of a 5-6 year contract that is a top 50 guy is a boon compared to a similar guy you paid 40-50 million or more for because you picked him in the top 10-15 or so. Let's you keep more of your core players that deserve to be kept, or splashed into free agency.
Thus the 34th pick is a pretty good pick. You just have to hit on it.