Could the US beat Russia in war?

If nuclear weapons were used, no. Both would lose, along with every other country in the world.

If nuclear weapons were not used, it would depend on who was attacking who.
Any invasion of Russia would have to be a perfectly executed strike, crushing all major and organised resistance within months, otherwise it becomes a war of attrition and there is plenty of history to show what happens then.
An invasion of the US would have to cross several oceans, or proceed through other countries (who would of course, not be friendly to any invading force). Hence, it is unlikely a decent foothold could be established.