It's wierd that they didn't. The americans at that time had a plan to conquer all the lands in north america to prevent the continent from looking like europe.
Early America was a cluster-F, to say the least. In short, the further North once settled in North American, the more loyal one was to the Brit Empire. Obviously, I am simplifying it, but most former Brits/New Americans had growing dissent with the Brit empire because of slavery, taxation, etc. Whereas, Brits/Future Canadians more than likely didn't have similar complaints. Another post made an amazing post about failed attempts, but I consider it a part of USA vs. Brit, especially since Canada didn't become its own nation until mid-to-late 19th.
The idea of manifest destiny came shortly after annexing Texas. It mostly justified Westward Expansion.