Not sure desperate is the right word to use. If there was any desperation to these negotiations, from either side, than this deal would have been done a long time ago. Obviously Yzerman is being careful about using up too much of the cap. That cap space is extremely valuable whether it's used on 91 or other core pieces. And either way for Stamkos, wherever he's playing in October, he's still going to make a lot of money.
Something I've been thinking about is that July 1st doesn't have to be a deadline. Stammer becomes a UFA on that day, but that doesn't mean both parties can't still negotiate with each other. It depends how much they still want to make this work.
Now in a perfect world if you're a GM or a pending UFA, you want a decision made before then. If you're Yzerman, you want this contract done or know it's definitely not going to happen so you can move on, prepared for Day 1 of free agency, and attack the rest of your GM checklist accordingly. Same with Stammer. If there's no deal with TB, you want to switch your attention to the market and sign early with another team before they too try filling up the rest of their rosters. Waiting too long will jeopardize the number of teams you want to go to, and the amount of money they'll throw your way.
So maybe that doesn't even make sense. I guess I'm just hopeful since both sides have expressed they really want to get this done, that they'll eventually find a way to make it work, even if that means making this Stammergeddon last a little longer.