Assuming the bill passes Congress, and assuming the president or anyone else with sanity doesnt veto it and question the sanity of his peers then I see this plan getting sent to Canada, which of course declines to join the Union and tell the British they are a) worried about their southern neighbor, and b) think an invasion is imminent. The two are not mutually exclusive.
Hee hee, that's all quite true - although given the President in question would be Andrew Johnson, one can only wonder if he would welcome a juicy war scare with the British Empire as a nice break from , well, everything
about his accidental presidency.
On a less mischievous note, I was actually pondering something less a 'Hard Facts' Alternate History scenario and more what sort of satire a Mark Twain might have built upon the Annexation Bill's idea of a US Canada - it strikes me as a fairly interesting vehicle for a parody/pastiche of the Reconstruction Era (I'm not certain if this should be a satire on the North's good intentions being somewhat undermined by those eager to treat the South as a conquered province, rather than liberated States, or whether it would have been possible for a more Radical Republican author to skewer terrorist elements in the South by showing Canadians in the new states & territories work much the same sort of crooked mayhem on law-abiding citizens).
Bonus points if Irish-American carpetbaggers are shown sneering over Anglo-Canadian resistance to US occupation at some point!