No, I don't agree with you. The US isn't pushing for war with Russia at all. The left don't particularly want war. Hence why in the last 8 years there has only been a start of minor wars for the US rather than than two big ones under Bush. Obama tried to pull back from the anti-Islam sentiment, he hasn't done much with Russia either.
The right might want more war, it seems to be their thing, however they've got the "War on Terror" and ISIS to keep the people in their place and spend more and more money on the military. They don't need Russia.
In Syria the US bombed some Syrian forces. The Russian decided they had to have revenge for this act which appeared to either be a mistake, or someone duped the US into it. The Russians then went and attacks aid workers, killing them. I mean, seriously.
Why is Russia aiding Assad? It would see that any guy the US hates, is a friend of Putin's, so he went in to piss the US off. He knew he could get away with it, playing with people's lives because he doesn't care.