- The Revolutionaries, through some slightly better luck in the Canadian Campaign, manage to bring Canada into revolt against the British, and the end of the war sees the two united. Later, the Mexican-American War still breaks out, though the Americans are rather more ambitious, leading to a single continent spanning United States in North America...
IMHO its more tricky than that. Firstly, if Canada is also annexed, USA will probably be even harder to keep together than in OTL, with even more separatist movements and less of a British threat nearby (plus without the British loyalists, Canada will be French-majority, causing lots of strife as the Americans really hated the Quebecois at the time - see Quebec Act and its effects). IMHO its more likely for the Americans to conquer it in 1812. Furthermore, no matter when Canada is conquered, it automatically means much less immigration to Texas (hence the situation in one of my guess-the-pod maps, based on the premise of America winning the War of 1812, where Mexico retains its territories). By the time Canada is settled enough, so will be Texas - by Mexicans (and maybe by Germans). So chances are there won't even be a Mexican-American War. Oh, and the inclusion of Canada will also disbalance the Union, resulting in either earlier and more succesful Confederate seccession, either the South being crushed quickly, maybe even without a war.
Also, gobbling up the entire Mexico in one war... IMHO USA - of the 1840s, anyway - might simply fail to digest it. It might just die.
IMHO to unite North America USA should evolve as it did in OTL for a while, possibly up to the very late 19th century. Then we need to somehow shake it up economically and socially as to encourage greater political radicalism. And then it could simply conquer Canada and Mexico. I think Theodore Roosevelt, given the right geopolitical situation, could do just that.
EDIT: One more thought. This might have interesting effects on the development of Australia as the British loyalists have to go SOMEWHERE... Alternatively, they might go to South Africa. Actually, if they go to it immediately after the war and pull a filibuster, guess what we get.
Nobody would be expecting either of these and likely half the players would quit, but it could be highly interesting.

EQ (or was it Sheep?) actually did a WWII scenario based on that, and indeed, as soon as the first update mentioned Atvar out of the blue, shocked, outraged NESers begun quiting. The NES died within minutes, I'm afraid...