I think in relative terms, it will be fairly quick - but that only means that most, if not all the core is only gone by the beginning of next season.
I expect Winnik, and probably at least one core/active member will be gone. Most likely to go with Winnik at the deadline are Bozak, Lupul if anyone bites on that, Phaneuf. But it could be anyone really if the right deal materialises.
At the draft, some deals will be offered, but I sincerely doubt we actually deal anyone for a draft pick. Everyone will hold on tight to their picks.
In the summer, I expect most of the core to be gone.
Of the current roster, if looking at the top 3 lines and top 6 D, and goalies too, I expect only the following to remain:
Kadri, JVR, Komarov, Holland, Clarkson
Reilly, Gardiner, maybe Polak (Holzer will still be there too)
Bernier
If one or two of the core are still there - with the exception of Kessel or Phaneuf - I'm ok with it, it just means that we couldn't get good value for them, and we can pump them up for a trade midseason next year.
It'll be one more "burnt" year (next season), and we should draft top 10 again. The year afterward, we might actually start having a competetive, developing team. Year after, who knows? Playoffs and beyond, I hope.