The current government likes to make a big show of parading through the North with military exercises and stuff, but the average Canadian isn't really concerned with what's going on. There are disputes between Canada and Russia about where the actual border is based on international waters and the location of the continental shelf. If I recall correctly, Russia had one of their submarines plant a flag on the ocean floor a few years ago that resulted in a lot of posturing on both sides. There's a ton of oil up there, but it's too expensive to drill right now so no one is really fighting over anything.
For most people, the islands are so far away that they don't really matter. If anything actually happened, it wouldn't take much to get Canadians all riled up about it, though. There's some island near Greenland that had some Danish sailors plant a flag on, so we sent a bunch of guys there to kick it over. This resulted in a lot of chest-puffing and calls to invade Denmark.
Since then, we've pretty much agreed to split the island in half.