I know all of this. I still stand by my statement. By the time of World War One ( which is what I was referring to by "European Wars" and was doing so under the apprehension that US history had unfolded as it did in reality up to this point ) the US had become unassailable. Our navy was to the point where any attempted forcing of an invasion on either coast would have been so prohibitively costly as to be impossible to attempt by any world powers. Additionally, US industry was substantial and our population was continuing to grow at a much faster rate than that of Britain. US population in 1900 was 76,212,168 and increased to 92,226,496 in 1910. Britain on the other hand had a population of 41,154,600 in 1900 which rose to only 44,915,900 by 1910. Now admittedly the British Empire in total at that time had a population of over 400,000,000 but more than 70% of that was in India, with another 10% being in British Africa, and only 10% being in the British Isles proper. While these territories could be called upon to fill manpower shortages doing so would take time and would also necessitate profound changes for Britain's governance of these people ; Indians wouldn't have tolerated wholesale conscription without significant concessions, and I doubt the Africans would be willing to do the same either.
Let me be clear though, the US was not the juggernaut that it would become after WWII, let alone the technological powerhouse it is today. But it was a strong enough nation with a powerful enough navy, resolute enough national identity, large enough population, substantial enough industrial base, and plentiful enough natural resources as to be capable of withstanding any assault from the super power of the world in 1914 : the British Empire. America's deficiency at the time was its pitifully underfunded Army however it was demonstrated that, when called upon, the US could forge a large and professional army in a relatively short time.
Without any suitable staging ground from which to launch an invasion of the US mainland the only plausible point of attack of the US from Britain would have been from Canada. Indeed this was the source of their success in the war of 1812. But the US of 1914 was not the US of 1814. An invasion of America from Canada in 1914 would require significantly more men and resources to accomplish and the movement of these forces to Canada from Britain would not go unnoticed by the American military. This buildup would be met with a similar buildup by America and while the British would have the advantage in experience, training, and equipment the US would have the advantage in manpower and logistics - Britain of course needing to ship most of its war materiel to Canada while the US could manufacture most of its equipment almost right on the front lines given where the likely fighting would be.
On that point, in 1914 most of the US-Canadian border was barely inhabited wilderness with minimal connection to roads and rail networks outside of a few select hubs. Most of Canada's infrastructure was concentrated in the eastern population centers of Ontario and Quebec, mirrored by the American population centers of New York, New England, Ohio, Pennsylvania, and Michigan. While the possibility of small incursion from more remote areas of Canada as well as a possibility of a smaller-scale attack from Vancouver into Washington exists the US benefits from a similar strength of Russia : land. The US can sacrifice raw acreage in the West and Midwest and keep fighting. British forces might be able to penetrate relatively deeply even with only small contingents from Manitoba, Saskatchewan, Alberta, and British Columbia but the strategic effect of these attacks would be minimal and extended supply lines would quickly render them nonviable.
The fight would be concentrated in the Eastern part of the continent, with Michigan, Upstate New York, and New England likely facing the brunt of the conflict due to the proximity to Ontario and Quebec. This allows the US Army and the various National Guard forces to concentrate their forces into a relatively narrow front, with a possible side-theater in Washington state ; cavalry and other light units would be sufficient to provide flexible defense for the rest of the country. The US Navy would likely avoid engaging in any pitched battles with the Royal Navy and instead remain on alert to respond to any attempted landings on the coasts. A contested landing would result in huge casualties taken by the attacker even if it did result in the destruction of most of the US Navy the manpower and equipment costs would likely be too dear for Britain to attempt. A battered Royal Navy leaves them open to attack from Germany, France, or anyone else.
Given what we know of the events of the First World War I can not imagine the British land campaign fairing well. Much of the border areas even in the populated Eastern part of the US and Canada is rough country providing amble opportunities for the defenders to entrench themselves. My biggest concern would be the paucity of American artillery but given how much time the Americans ought to have had to prepare for this after seeing the buildup of British forces in Canada I believe that some semblance of parity could be achieved through domestic manufacture and foreign purchases : the Germans would love to see their guns used against the British without any of their own people spilling their blood.
All in all I think this would be so difficult of an undertaking that I do not believe the British would ever have attempted this.
