Just like fishercob said, we don't have to worry about that. While the Bulls could officially miss out on LeBron by then, they could still go for Wade, Bosh, Johnson, Boozer, Stoudemire, etc. Pair up any of those two and add them with Rose, Noah, Deng, and their bench, and you have a damn good team in the making. This offseason has made everyone think that you need an absolute elite player to succeed, but that's still a great team. Unless you have a perfectly designed team in place, you need to have one HOF caliber player on your roster these days, but a Rose/Noah/Johnson/Boozer squad has a **** of talent, and one of them could really develop into a HOF caliber player in that setting. Getting Johnson/Boozer when the fans have their hopes up for James/Bosh will seem like a letdown, but they have to step back and realize that their team just became unbelievably better.
Anyways, if LeBron is already gone, and those other top tier FAs are as well by July 8th, then yes, theoretically the Bulls could back out of the deal, and we'd be "screwed". However, a part of me believes there's at least some semblance of a written agreement to execute the basic trade agreed on. Also, it's really not the end of the world if they did back out of the deal. We don't have Hinrich or Seraphin, but that's right where we started from. While I'd obviously much rather have them than not, we'll live.
And yeah, if James agrees to go to the Bulls, as well as Bosh or another max player before July 8th, then theoretically we could blackmail them into giving us additional assets, or we could simply say, "eh, nevermind, we'd rather them go to the knicks/cavs/heat". Now again, that's not gonna happen, but in theory, it could.
The Bulls have a lot more to lose than we do if one of us backs out.
Now, if LeBron throws everybody a curveball and decides he wants to go to the Wizards, then by all means Ernie, run as far away from that deal as you can. They can have Seraphin
