I don't know how this would play out but my best guess would be The USA would do well early on. We have poured more resources into our military so we would initially gain the upper hand.
If it gets long and drawn out though I think we will start to see a shift due to China and Russia being able to throw more manpower/resources against. China has 1.35 billion people or something close to that. They have a strong economy and while Russia is a baby compared to the soviet union they can still pour in some vast resources as well.
So I could see a WW2 Germany Scenario happen where we just keep getting whittled down while two superpowers drain us of bodies and materials.
Of course there are many variables that would need to be accounted for such as weather, location, intelligence gathering, other logistics such as food, water, supplies.