It might be possible but there are some tradeoffs. You're going to piss off all of those NATO states who are in it pretty much to avoid conflict with Russia because Russia knows not to fuck with our friends. If the US could somehow get the NATO states and Russia on friendlier terms in some fantasy land this might work, but that is very unlikely given European history.

The only common issue I could see Russia and the US possibly agreeing on in terms of world power is dealing with the threat of Islamic terrorism and possibly dealing with Chinese aggression (I honestly don't know what Russia and China's current relationship is like but it was strained when the Chinese communists basically told the USSR to fuck off, correct?). And even then, there are stark differences. Russia's methods for dealing with Islamic terrorism make Donald Trump's plan of "kill their families" look like some Mary Had a Little Lamb shit. Not to mention while the US deals with Islamic terrorists out of national security interests in not wanting these states to take over and threaten the West on a large scale (such as getting their hands on a nuke in Pakistan or threatening Israel on a much more serious scale than they already do). Russia does it with the extra intention of propping up assholes like Assad who are nice puppets for Putin and the Kremlin. Not saying it would be prudent for the US to topple more regimes, but we don't have to be complicit in Assad's terrible actions either. Russia bombs more anti-Assad rebels than just ISIS agents.

Personally, I'd be pretty apalled to see the US embracing the Russians like friends. This is pretty much reneging on our commitments to our European allies who are on the front lines and have seen first hand what the Russians desire and what they are capable of. Putin is not a friend to have, he only wants to control you and will stab you in the back if you step out of line. It is scary that he "admires" Trump, that tells me he thinks Trump is weak and can be manipulated.