A few reporters wrote while the Olympics were going that Dame had committed to Chauncey and Neil that he would give them a chance to prove themselves. Those writers speculated that he would start the season with the team and see how the team is performing. If they are performing the way they have in the past (losing to the best in the league) then he'd ask out with plenty of time before the trade deadline.
So the team has until probably some time between the beginning of January and the beginning of February to show Dame that they're a contender. If Olshey isn't going to make a big move between now and then, he should trade Dame now before the trade demand gets leaked which would slightly hurt his value.
This is not on Dame, I guarantee the guy had been on Olshey about improving the team for a while before he went public. I guarantee there are ways that even right now, Olshey can improve this roster to the point Dame will stay. If Olshey does nothing and Chauncey can't pull off some sort of miracle, I personally think Dame will be gone at the deadline. Why on earth would the guy talk about urgency and then give the team two off seasons with a full season in between to improve?