Douglas
OK, a bit more detail to work with. Going to be interesting for the allies going against an enlarged Germany, Russia and the rump US. However would be surprised that such a combination at this point would be a serious threat to Britain and allies at sea.
With the main N American fronts the US is very confident to pick fights with both Britain and the CSA at the same time, even with Britain already involved in a sizeable war. This suggests their going to be the primary aggressor on most fronts. Whether they have the resources to actually do this is another matter. In OTL WWI, when the initial quick victory failed to materials every nation, even the most militarised, quickly ran into shortages. Also, presuming that the US has large scale immigration as OTL, although probably somewhat less than OTL, they would [or should] have doubts on the willingness of many of those to fight for US wars of expansion, especially with Britain and Italy on the other side. However I would expect the US to do the bulk of the attacking, at least in the 1st year or two. Given the culture of the offensive that was widespread in the western world at the time and probably more so in N America than elsewhere I suspect the CSA will also try some attacks. Britain/Canada less so because they have less resources and commitments elsewhere. Also it sounds like there's not an existing alliance with the CSA so no combined action is likely early on.
This is all pretty much correct. I wonder whether or not it would be better for the US to try to overrun the British quickly, but the way I've posited this war, the main effort at war's opening will be to the South.
I would expect by far the heaviest fighting to be on the east of the front as that's where the bulk of the population and industrial base for each side is. Also Washington could be a red flag for the north. Furthermore, if the south is likely to be able to make a decisive offensive it would again be in the east. Both because their main resource base is here and because its here they could do most damage to the north.
Oddly enough, the only theater in which the US is likely to gain significant ground, by my judging at least, is in the far East near Washington. Assuming that the US mobilized troops from the New England states, New York, and eastern Pennsylvania are the ones used on this front, and that a further 100,000 of these are used for defense against the Canadians or in slow cautious advances, the US will have (assuming 2,000,000 men strength overall after mobilization) 750,000 troops to deploy in the relatively narrow theater between the Atlantic Ocean and the Appalachian mountains. The CSA, assuming a more drawn-out but also more extreme (greater % of white males) mobilization, can still only get 500,000 troops to the Eastern theater even if every soldier from the states touching the Atlantic gets to the front. Earlier in this thread I posited five different plans for the CS to consider, but after some more consideration, the first two are unlikely to occur because of the disparity in numbers and the more rapid speed of US mobilization.
Counting the US soldiers from western Pennsylvania, Ohio, Michigan, and Indiana gives me a total of roughly 520,000 men to be deployed along and across the Ohio River. How difficult is it going to be to cross the Ohio River in the first stages of the war? Turtledove discussed it, but with a bit of handwaving. Is the river going to be a barrier to operations, if, say, barges and what-not haven't been collected as part of mobilization for an amphibious crossing? Facing the US will probably be the 425,000 or so more slowly mobilized Confederates from all of the remaining states east of the Mississippi River.
The most interesting theater that I ran into was the Trans-Mississippi Kansas-Missouri theater. Missouri and Texas are the largest Confederate states in terms of population, which results in equality on this front against the US, though, of course, not at the very opening of war. The US troops from Illinois, Wisconsin, Minnesota, and Iowa number 500,000. I have no idea how this front will play out, especially with the big salient of Confederate territory...any takers?
I'm guess there wouldn't be heavy fighting in the west. They don't have the population base on either side nor probably the ability to get larger forces there. Also if only one US trans-continental, not established until the 1890's they probably don't have a line going deep into their exposed pocket in the SW, which is nearly encircled by CSA territory. Hence an attack on California from there would be unlikely. [Could see them having a line to the neck of the area to prevent the south cutting it off]. Most likely activity here might be an attempt by the CSA and possibly Canada to link up by cutting off Washington state/territory, but would expect the US to oppose this. Also possibly attacking on rail lines by small raiding forces in the thinly populated prairies. [Presuming that there is also a Canadian trans-continental]. Here you could well have a war of manoeuvre with small cavalry forces hitting each other's vulnerable targets.
Agreed. Mobilizing everything west of what has already been mentioned leads to a grand total of 125,000 US and 100,000 CS troops for this entire theater. The Canadians may well hold on this front, even if the US goes on the defensive everywhere else in the West.
In the longer term, as you say the US will be vulnerable to a British blockage, especially if it can deny the US access to nitrates. That would increasingly cripple the US army. [If really nasty for them they manage to build up a large artillery force and train the men to overcome defences just in time for them to become largely useless due to lack of propellant.

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This is very possible, but the British may well be vulnerable to losing access to the same resources due to surface raiders of their opponents.
In all areas the relative efficiency and tactics of the various powers will have a big impact. If anyone tries to force a breakthrough against a reasonable depth of defence, even with just repeater rifles let alone Maxims, their going to be in for a world of hurt.
Steve
That especially could happen in Europe, though the Eastern front in America seems to be the only place that could suffer from a certain kind of trench warfare.