We wouldn't do a ground invasion of Russia. We'd break Russia's capability to make war from the air mostly, before encircling and destroying Russian ground forces in Eastern Europe.
Russia would get hit with more long range (conventional) missiles than any other country in the history of man ever has, but US Infantry and Armor wouldn't be rolling onto Moscow.
As for the US commitment to it, it absolutely would. If the US doesn't honor it's security commitment, our entire global defense strategy collapses. In many ways, a limited conflict with Russia would be the essential test case of that commitment.