If the numbers from earlier reports are correct, I expect Damon to sign very shortly. He would be stupid not to, at least he won't look like a complete ass because he'll be getting the same money he could have gotten earlier this winter.
Still, I'm sure he's kicking himself for this--I have to imagine he'd rather play for the Yankees than the Tigers. The only thing that could save him from that is if the Tigers finish better than the Yankees do this year, but I don't think that will happen.