I don't even say this with my typical Murican bravado, I'm being entirely realistic - it would be over in a few weeks, with Canada seeing such significant losses they either lost their functional military or saw so many deaths they sued for peace.
There are a lot of reasons this would take place but the most important is that, even in the midst of a civil insurrection scenario, most Americans wouldn't actually want to shoot other Americans, and the leafs would still be the foreign force invading, so wouldn't pose the same moral quandary. Any burgers who didn't want to end up shooting someone they used to play CoD on LAN with, would opt to go fight the invaders instead. It would also result in people who didn't even want to have anything to do with the civil war shit jumping in because, invaders.
And this isn't even going into, well, the Canadian military of today is a joke. I will give credit where credit is due, they were important allies in WW2 especially in forming the FSSF. But modern Canadian military could probably be defeated by a determined enough herd of wildlife, a la Aussies vs Emus.