They signed fourth-round pick Andre Williams and fifth-round pick Nat Berhe last week, so the only Giants draft pick yet unsigned is third-rounder Jay Bromley, who will sign very soon, maybe even today.
So yeah, within two weeks of the end of the draft, everybody should be signed and working out with the team. Same with every other team around the league. These guys sign very quickly, with no drama.
You likely remember a time when this was not the case -- when draft-pick negotiations would drag on through the summer and threaten to keep the new guys out of training camp as agents and teams haggled over the details. But the NFL and the NFLPA agreed, in the last CBA negotiations, to an institutional change that eliminated the drama.
Draft-pick contracts are now "slotted," with predetermined amounts assigned to each pick based on what the player picked in that spot got in prior years. The signing bonuses are even flat, which means that Beckham got the same $5,888,144 signing bonus as last year's No. 12 overall pick (Raiders cornerback D.J. Hayden), 2012's No. 12 overall pick (Eagles defensive tackle Fletcher Cox) and 2011's No. 12 overall pick (Vikings quarterback Christian Ponder). The annual minimums go up by around $20,000 in each draft, but the signing bonus stays the same. The total value of Beckham's deal should be right around $10.4 million for four years, with that fifth-year team option for 2018 that has to be picked up by May of 2017.
The reason for this is that one of the things the owners wanted out of the last labor deal was cost certainty on rookie contracts, which they felt were getting out of hand at the top of the draft. The union agreed to a rookie pay scale in exchange for other things it wanted, like improved health benefits for players and their families and reduced workloads in the offseason, and on the stipulation that the money saved would go to veterans. Veteran minimums have risen, and the new deal instituted a salary "floor" that requires teams to spend a certain percentage of their cap money each year.
The end result is a complete lack of drama in the contract negotiations for Giants rookies and all other rookies around the league, who are getting signed and into team facilities as quickly as the paperwork can get done.