Nuclear War with Russia would inevitably draw in North Korea and China. In Annie Jacobsen's Nuclear War: A Scenario, the president is basically given an ala carte set of options with different levels of mass destruction. The problem is that even the most "minimal" response to an attack , would result in the fallout and subsequent death of citizens in nations not directly involved; this would be treated as an act of war and lead to their subsequent response. Which would lead to further escalation.

Additionally, given the assumed targets in America, Russia, North Korea, or China involve military facilities and, next in the list, nuclear reactors. Just one hit near a reactor would lead to a meltdown and a plume of radioactive smoke that would destroy any and all capability for life in a massive radius (a collapse in the energy grid would be the least of our problems).

In short, anything above a hot conventional war would lead to catastrophic consequences to the the human race.