From Brilliant Maps: Making Sense of the World, One Map at a Time (hat tip: Tim Furnish): a map of what North America might have looked like if the Annexation Bill of 1866 had passed.
The bill would have authorized the President of the United States to, subject to the agreement of the governments of the British provinces:
publish by proclamation that, from the date thereof, the States of Nova Scotia, New Brunswick, Canada East, and Canada West, and the Territories of Selkirk, Saskatchewan, and Columbia, with limits and rights as by the act defined, are constituted and admitted as States and Territories of the United States of America.
Or to put it more simply, the bill would have annexed Canada, before Canada became a country.
I believe that annexing Canada, as a long-term policy goal of the United States, was only abandoned following the First World War. Throughout the nineteenth century, I understand, the USA saw British North America in the same way that the PRC views Taiwan, or the Republic of Ireland views Northern Ireland: as the rump state of the previous regime, and thus morally illegitimate.
Although I note that the bill does not mention Newfoundland, which had become crown colony in 1854 and was never part of Canada East; the map should probably reflect that.