But you have to remember, you started out with an easy target...the second largest country in the world. Now with only 29 million people, they would soon run out of soldiers. Except for the millions and millions of troops flying in from Russia, China, India, the Common Wealth and African nations. Also remember the war is in North America, and that is where the bombs will fall, and with every bomb NA becomes less and less able to recover it's infrastructure and continue the fight.
First problem is the power grid between Canada and the US is both connected and open. Pipe lines are an easy target and without oil sands oil America runs out in about two years, if not sooner. Pounding Canada doesn't stop the world from resupplying both troops and arsenal. There is no way to blockade all of the Canadian shorelines or north.
It would be a brutal long four or five years, but in the end, because of attrition the US would loose. There is an old barroom saying: "I don't care if you want to fight but take it outside"
I think it is very hard to say since modern armies have never faced off against each other in such a way (and are hardly designed to). Amphibious assault ain't so easy. It is *much* easier to defend from an entrenched position rather than attack one. There's a reason why
Unternehmen Seelöwe was never undertaken. The US has a vast population and vast access to resources, and a battle-hardened military. Especially if we stick to non-nuclear, the US has a sizeable military-technological advantage. It is hardly clear that such an invasion of the US would be feasible. Ship-based transport seems unfeasible to me, in an age of rockets and stealth bombers, and nuclear submarines (where I believe the US still reigns supreme). So how are the armies of the world suppose to land armor and troops without suffering *massive* casualties?
I don't think it is nearly as clear-cut to say what would happen in a 5-10 year war of attrition, if we are sticking only to conventional weapons.