They're both impossible and quite easy to fix for different reasons.
Montreal is harder to fix, but there are fewer roadblocks. Ottawa has much better talent to work with, but there are locker room problems, trade value problems, cap, ownership, and arena issues all of which gives them enormous hurdles.
Montreal would be fine if a competent GM took over. They don't need to "rebuild." There's nothing for them to sell-off, they have very good young guys in Drouin, Domi, Mete, and they are already picking 3OA, so if you want them to "rebuild" then you already have your wish. People need to shut up about the Weber contract. He's not particularly overpaid, and he is still a 1D. He plays a game that will age fine, has an excellent leadership résumé, and can gavone minutes in all situations. Those qualities make him an excellent guy to have sheltering a young and developing D corps. If they trade Pacioretty for a 1st at the coming deadline, retain on Gallegher/Shaw and trade them for assets, and have the bad year resulting in a high pick we expect them to, they will be well on their way to a successful rebuild.
Ottawa is a mess because even if they were able to retain all of Karlsson, Hoffman, Duchene and Stone, that is not a Cup winning core. In the pipeline, Brown has struggled, White hasn't been impressive, and while Chabot looks great, they lack real talent coming up. Hypothetically they could trade Hoffman, Karlsson and Duchene (next year) for a haul of picks, prospects, and stop gap veterans to go through a speedy and well done rebuild a la Tornoto and (currently) NYR. Problem is that Karlsson and Hoffman's trade values have surely plummeted. And it's not like Melnyk has any plans to help the team out in any way. Throw on top of that they are a small market team with an older arena in a terrible location and have a furious fanbase...even going through a hypothetically successful rebuild might doom the team financially and make it all for not.