The most likely outcome? Trump continues to says stupid things for a while about Canada becoming another state, His idea gains no real popular support among the American people. He continues to fight the court system in his own country because his administration simply refuses or is incapable of complying with the law, even as his Republican congress is furiously rewriting the law to favor his policies. Americans’ opinions of Canada will drop a bit because of Trump’s rhetoric but Trump is good at making enemies, so Americans’ vitriol will be spread among targets far and wide, and Canada will catch only a little of it. Canadians’ opinions of Americans will sink into the toilet. Both countries will subtly make visitors from the other feel unwelcome, which will extend to things like increased friction at border crossings in both directions as the countries stop cooperating on things like Nexus and generally just harass visitors at the border. Trade between the nations will drop precipitously at first, then begin to regrow only very slowly.
The US economy continues to melt down due to tariffs and general uncertainty over whether the US will stand behind its debts. Congress starts working diligently on tax cuts while there are still some tax receipts to stop collecting. Then, Republicans will lose control of the house in the next election and the idea that government can do anything in America will seem like a pipe dream. After a several protracted fights about the budget, the debt limit, taxes, and perhaps one or two more impeachments, Trump will be tired. He will have long stopped talking about Canada, until someday somebody asks him about his intentions, and he says, “Canada? Nobody even goes there anymore because it’s filled with socialists who tanked their economy.”
In the meantime, Canada is shifting its trade policy to favor Europe. It’s shifting its defense policy, at tremendous cost, to potentially resist a southern invasion. It’s seeking intelligence sources other than the US. It’s investing in new arms from its own defense industry and from Europe. it does this for 5-20 years. When an invasion doesn’t come in that time, and during some future economic downturn in Canada, the level of defense spending will be used as populist wedge issue of whatever party is out of power and Canada will begin to scale back.
Within a generation, almost all of this will be forgotten by both sides, but the level of camaraderie between the nations will settle at a new lower level. But also in the meantime, Russia will have rebuilt its military and China will have wildly expanded its global influence by filling two or three critical niches abandoned by America: reliable trading partner, backer of stable currency and debt instruments, and provider of foreign aid.
I’m not saying war between the US is impossible. I think it’s just way less likely than the US just making ruinous trade and foreign policy decisions by stepping on its own dick. ETA: And, the US’s idiocy will force Canada to do the same.