Excellent....and a complete blindsider !
The book "A World Aflame" by Amanda Foreman gives lots of background about what was going on between Britain and America during that period. We came astonishingly close to war both because of the seemingly belligerent political stance set by the US and some shockingly poorly managed diplomatic incidents.
With France in Mexico and Britain in Canada there is a wealth of "what if's" waiting to be investigated.
More!!

Actions have consequences.
In 1917 there recruits for what we call today WW1 noted in the newspapers who had enlisted and were looking forward to fighting the English. Had there been a war in the 1860s there might have been some problems getting enthusiastic recruits to fight versus Germany.
Of course the Zimmermann Telegraph/Note Affair http://en.wikipedia.org/wiki/Zimmermann_Telegram was the best British propaganda tool the Germans could have come up with.
Edit: (from above link)
Popular sentiment in the U.S. at that time was anti-Mexican as well as anti-German, while Mexico was anti-American and in some cases, anti-European.[10] General "Black Jack" Pershing had long been chasing the revolutionary Pancho Villa, who had carried out several cross-border raids. News of the Telegram further inflamed tensions between the U.S. and Mexico.
On the other hand, there was also a notable anti-British sentiment in the U.S., particularly among German- and Irish-Americans (the latter of whom were most recently infuriated at the British by their brutally swift suppression of the 1916 Easter Rising in Dublin). Until the early months of 1917, American press coverage of Britain and France was not much more sympathetic than press coverage of Germany. Above all, the vast majority of Americans wished to avoid the conflict in Europe. Since the public had been told (untruthfully) that the telegram had been stolen in a deciphered form in Mexico, at first the message was widely believed to be an elaborate forgery perpetrated by British intelligence. This belief, which was not restricted to pacifist and pro-German lobbies, was promoted by German and Mexican diplomats, and by some American papers, especially the Hearst press empire. This might have presented the Wilson administration with a dilemma—with the evidence the U.S. government had been confidentially provided by the British, Wilson quickly realized the message was genuine, but he could not make the evidence he had public without compromising the British codebreaking operation.
However, any doubts as to the authenticity of the telegram were removed by Arthur Zimmermann himself. First at a press conference on 3 March 1917, he told an American journalist, "I cannot deny it. It is true." Then, on 29 March 1917, Zimmermann gave a speech in which he admitted the telegram was genuine.[11] Zimmermann hoped Americans would understand the idea was that Germany would only fund Mexico's war with the United States in the event of American entry into World War I.
On 31 January, Germany resumed "unrestricted" submarine warfare, which caused many civilian deaths, including American passengers on British ships. This brought about a wave of anti-German sentiment that spread like wildfire. The Telegram greatly increased this feeling. Besides the highly provocative anti-U.S. proposal to Mexico, the Telegram also mentioned "ruthless employment of our submarines."[12] It was perceived as especially offensive that the coded Telegram had been transmitted via the U.S. embassy in Berlin and the U.S.-operated cable from Denmark.
Gracias,
Glenn