I think if they fail to sign Strasburg, everything they are trying to do to build a fan base will suffer tremendously. And that puts Strasburg and Boras in the driver's seat.
Personally I would not have drafted him. The track records of pitching phenoms taken in the draft are not good. The risk of injury alone is enough to make me steer clear. But all that is to be considered before you spend your pick.
At this point, they've raised their fans' hopes, and if they don't sign him, the GM will have to be fired to save face, just for starters. You can't go back-to-back years without signing your top pick and then try to convince fans to come out to watch a team that wins only 30% of its games on the premise that you're building for the future. Someone would have to take accountability for repeatedly drafting guys who won't sign, when guys who would sign were right there for the taking (and got taken by your competition).
Bottom line, they should've talked to him pre-draft, and if they couldn't reach an agreement pre-draft, they shouldn't have taken him. Let him go be the next Mark Prior at the Yankees' expense.
But now that they've taken the plunge, they're all in. They can play the brinkmanship game all they want, by Aug. 17 they have to give him what he wants or they're toast.