Well, alright, let's deal with the War of 1812 -- possibly best described as "Boy, did we pick a bad year to declare war on Britain!" If the British really had continued to be distracted by Napoleon as much as they had been -- if Napoleon doesn't self-destruct in Russia immediately following James Madison's exceedingly ill-timed declaration of War -- well, you know you can kiss Canada goodbye. The point is the British already had a huge military machine in place, that they could quite conveniently and almost immediately transfer to the North American theater of war, as soon as Napoleon succeeds in self-liquidating his own Grande Armee.
This is completely wrong. Britain remained heavily committed to the Peninsular theatre until the defeat of Napoleon in April 1814, as well as engaging in secondary theatres (e.g. the 7,000 men sent to the Netherlands in late 1813, who later fought at Bergen-op-Zoom). This is made patently obvious by the number of British regular infantry battalions in Canada and the Maritimes. In June 1812 there are 8 infantry battalions present: three more are sent during the course of 1812, and eight in 1813. In 1814, after the defeat of Napoleon, 22 battalions are despatched, a reinforcement which more than doubles the number of regular infantry battalions present in the theatre.
As of April 1814, there are 19 infantry battalions in British North America and 67 in Wellington's Peninsular army. What this demonstrates is that the US enjoys just under two years of fighting Britain while she's distracted by Napoleon, and conspicuously fails to make any progress in annexing Canada during that time.