I actually think you should focus on cooperation with China. There's a much higher need for cooperation with China, as relations have been strained due to military exercises, debt etc etc. We're no longer in the Cold War and the U.S-Russia have had much better diplomatic relations than the U.S. has with Beijing. Russia and the U.S. have START, collaboration on Iran, etc. There just isn't that relationship with China..China has replaced Russia as a bigger "threat" (I don't mean to threat con, lol). Not to mention China's greatly larger economy and the largest land army. I think the U.S. has a bigger incentive to improve relations with China than with Russia.
This is an interesting article that I saw today: http://online.wsj.com/article/SB10001424052702303678704576442400450218990.html?mod=googlenews_wsj