Rivalry between US and British imperialism will certainly affect the American political scene. If the PoD is sometime during TR's OTL presidency, we could see him running again in 1908 or a GOP nominee who is more interventionist (i.e., not Taft). In order to differentiate themselves from "Republican imperialism", I can see the Democratic Party become more Bryanian (if that is a word) and less progressive.
I think to actually get the U.S in war you want to start with earlier PODs. I am compiling notes right now, for a TL based around the idea of a second Mexican Empire surviving aswell as other US and British diplomatic incidents. I think I'll also have other things to change the war severely, that have to do with Italy.
EDIT: I've always been a fan of the Progressive Party, and TR, so I'm sure I'll find a way to ensure the Republicans split. The Democratic progressives split between Wilson and TR
if I remember correctly, with Wilson getting some ~40% of the vote OTL. Of course with different PODs and butterflys things 'll be different. What is interesting is that the U.S will be fighting a two front war, (assuming 2nd Mex. Empire) one in Mexico and one in Canada.