Magic thing called NATO and the UN that would join the US.
And there is a big difference between defeating a Nation in battle and invading/conquering their homeland. If Nukes were not used the war would result in stalemate neither side would have the strength to conquer the others homeland.
As for other powers helping Russia:
I doubt the Chinese would join the war, the US owes them a sizable amount of money from loans, if they attacked the US they would lose all that money forever. (its the main reason the Ottoman Empire joined Germany during WW1 to write off its debt to the Allies)
North Korea may exploit the US being busy elsewhere to invade the South.
Iran, at the moment I doubt they would bother, there more focused on the ISIS terrorist group/new nation forming on their borders.
Syria, Same main problem as Iran, except ISIS is within their borders already.
Various terrorist groups, that hate the US would not work with the Russians but would take advantage of the situation to expand their influence while the the US and Russia fight.
And if either side did start to lose they would threaten the use of their Nuclear arsenal, either force a peace treaty or cause nuclear Armageddon.
But a war between the two powers, would take a significant event to trigger and while its possible, until a highly effective countermeasure for Nuclear missiles/Nuclear weapons in general is developed, I doubt any Nation is going to be stupid enough to start another world war/try to conquer the world.
Military technology aside, the amount of privately owned munitions would make any occupation impossible. Secondly, if another country attacked the US, Canada and Great Britain (and many others) would also declare war the same day on the invader. Historically, Canada is no slouch militarily when necessary. We (and I) would be in the fight within 24 hours.
You could get rid of our (much more advanced, trained, and well equipped) military and no country could maintain a hold on the continental U.S for very long, it would be too expensive and complicated. The vastness of the country, along with the dramatic changes in weather conditions and terrain from one side of the coast to the other, as well as enormous, undefended borders both north and south, (not to mention our allies) would be a nail in the coffin to any invader.
As Lincoln put it in the Lyceum address:
"How then shall we perform it?--At what point shall we expect the approach of danger? By what means shall we fortify against it?-- Shall we expect some transatlantic military giant, to step the Ocean, and crush us at a blow? Never!--All the armies of Europe, Asia and Africa combined, with all the treasure of the earth (our own excepted) in their military chest; with a Buonaparte for a commander, could not by force, take a drink from the Ohio, or make a track on the Blue Ridge, in a trial of a thousand years.
At what point then is the approach of danger to be expected? I answer, if it ever reach us, it must spring up amongst us. It cannot come from abroad. If destruction be our lot, we must ourselves be its author and finisher. As a nation of freemen, we must live through all time, or die by suicide."
No truer words on the subject.
Russia may have a big army, but it does lack technology and funding. We know both governments spend a huge amount of money in their defense forces, but Russia doesn't have many strong allies except from China and North Korea. The US has the EU, Japan, most of Latin America, and many more.
Our allies would also come to back us. Ukraine was taken because they were not a part of Nato (foolish). The other Soviet states are and would back us under the treaty (not sure about Belarus). The U.S. has Britain, France, Germany, South Korea, Canada, and China. Russia really has no one. With the U.S. pounding them from the air, and the Allies pounding them on the ground together; Russia would surely lose.
Simply because there are too many countries that would be happy to break America teaming up with Russia. USA is not prepared for an attack on a large scale, people are clustered into tall cities and nobody is expecting to be attacked. USA is very comfortable where they are, a military attack would be quite devastating. And also America has no allies which would come to the rescue In a war against Russia. They would simply not want to get involved
Russia would do a large scale invasion. Something that we are not used to. We are used to fight in a technique like terrist. We would not be prepared to to fight face to face. It would be something that we would not be used to. ANother thing to consider is that the Russians first attack will be destroying all American Satellite, making the US blind from internet cell phones and radar.