Not impossible but very very likely. Not only are the Sens in 26th, but they are 13 points out of the playoffs. They would need to play around .750 hockey for the last 40ish games and hope that a few teams in and around 8th spot play .500 or worse. If that happens, they might squeek in.
Again, not completely impossible but not very likely either. I can see a fire sale in the Nation's Capital early in March.