In OTL...
In 1896, Venezuela had a border dispute with British Guiana which almost turned into a war with the United States when The british began to send troops to Guiana. The venezuelans realized that they could not fight a war with Britain, and so appealed to American President Grover Cleveland. Cleveland (citing the Monroe Doctrine) demanded that the British leave the Region or the United States would "by Every Means" force the British out.
The British and the Canadians began preparing for war. Reflecting on the possible war, the British Army decided that its plan would be to land troops at Boston or New York and make a "vigourous offensive gesture". However Britain would send no troops to Canada. As for the Royal Navy, it had no intention of conveying troops anywhere until the growing US navy was defeated.
However on October 3rd the Crisis was resolved when Britain decided to submit to the "Schomburgk Line".
what if the British were a little more ambitious and more Anti-American and the war does occur. I suppose the British Navy could successfully Defeat the American Navy and Land some Troops along the East Coast but What about Canada... would the Americans overrun it easily or would it Be a disaster like 1812.