Britain would probably agree to free navigation of the Mississippi, and this would be beneficial to the Americans. Also, Americans were at times during Canada's history the largest source of immigrants, and there was never any significant irredentist movement. Many who settled into Southern Ontario in the early 19th century were not even loyalists, simply people who wanted land. The same was true when the prairies were opened up to settlement in the early 20th century.
American Immigration to British North America
1781-1790 50,000 (Loyalists)
1791-1800 50,000
1801-1810 50,000
1811-1820 5,000 (2,500 black)
1821-1830 2,000
1831-1840 8,000 (5,000 black)
1841-1850 30,000 (5,000 black)
1851-1860 60,000 (20,000 black)
1861-1870 10,000
1871-1880 30,000
1881-1890 30,000
1891-1900 70,000
1901-1910 458,000
1911-1920 625,000
1921-1930 198,000
By 1914 the majority of the inhabitants in Alberta were American-born or had an American parent. In Saskatchewan they were a plurality and in British Columbia and Manitoba they were a large minority and there never was much of a push for incorporation to the United States.
As long as the British establish rule of law, protect property rights and are generous with doling out land grants, and establishing self-government, they do have a chance of keeping the territory. What might become a problem for the British, is if slavery spreads into Southern Louisiana, and it most likely will due to the cotton boom. If the British government attempts to force abolition, this might make many white settlers press for joining the union. That was the major sticking point with American settlers in Texas who began to resent the Mexican government's attempts at limiting the institution.