Nah, they would win the war almost immediately, there is no question. They could be in control of all our major urban centres within days.
The problem for them is not the war, i's the occupation. The occupation they would start losing almost immediately as well. But it will take them a long and painful time. Any puppet they set up will be weak and in need of American arms. They would probably employ mercenaries and ICE-type goons. But "might is right" would be their only justification and every one of those found bleeding in some back alley will be one more step down the path to them losing and pulling out. Terrorism will become our national passtime and it won't be contained north of the border, and it will almost certainly spill over to become an American blue-vs-red civil conflict. They will lose, but we will all suffer for a long time.