No matter the POD, no matter the casus belli, any war between the US and the UK before the ACW will cause a rift in American politics. During the War of 1812 OTL, most of the New England states basically sat out the war, wouldn't release their militias, covertly traded with the Brits, and during the Hartford Convention even considered secession. Also, in the reign of King Cotton, most of the trade of the southern states was directed towards the UK. This is the reason for the Nullification Crisis in the early 1830s, when the Jackson administration tried to impose tariffs on the very imported manufactured goods from England that the Deep South relied upon.
Had I the time and the patience to develop it, I've always had a pet AH project in my heart:
"1846 -- The Great North American Clusterfuck:" the US at war with the UK and Mexico at the same time over Oregon and Texas respectively, with secessionist rumblings in both the Northeast and the South.