I just don't know the players are thinking really. They've no leverage, and they're not going to gain any over time.
They are thinking like athletes who have had 1 thing drilled into their heads their entire life...win. The idea of settling for the best you can against someone you just can't beat is just something that doesn't register to them. They have been taught their entire life that they can beat anyone if they stick to it, and now they are seeing if they can take that mentality into the boardroom to take down Goliath.
Unfortunately I really think their best hope right now is a moral victory. If they can cause the owners to miss a few games, prove the point that they cannot be broken, and still get the same deal that was offered today (or something comparable), then they can walk away with their heads held high.
I will say one thing. I think Stern has done a pretty weak job over the last two weeks. I think he has painted the players into the corner with his very public pronouncements and deadlines. He has made it nearly impossible for the players to accept a deal before his "deadline", and still save face. Considering how proud these players are, that really killed things.
Now, I can't say that it would have changed anything, but I think there would have been a better chance of the players accepting a deal today, if Stern had played it a little differently, and allowed the players to accept a deal that the owners wanted, while still saving face themselves.
Now, their only way of "winning" was to call his bluff and hold strong through his deadline, and probably past November 15 (first checks), not to get anywhere in the negotiations, but to feel like they weren't simply played by Stern and the owners.