Unless the trading team is sending back cap hit, I don't think there will be many offers for the Rangers players.
Usually those looking to contend are somewhat near to the cap already. If they are looking to rent they will likely wait until the cap hit of the rental is more prorated. Plus without knowing for sure playoffs or not they could be giving up a lottery pick, so they'd want protection.
Even if a team is looking to extend the traded for, I think they have to wait until Jan 1st to do so.
I guess an injury could play a part, but even then most teams just suck it up or make some small trade for depth.
I would think the deadline is when the movement will take place, maybe a couple days/weeks before.
If the Rangers are already looking to sell I think they'd be better off just finding some way to motivate those they want to sell. Take away the youngest rookies competition for playing time, tell the to be sold players they are playing for their next contracts one way or another and this is their opportunity to cash in on it or not.