Better relations with Russia would be a nice thing. But if I were Putin I'd be cautious about cozying up to the world's most meddlesome nation. If suddenly the U.S. started acting nice, I'm not sure I'd trust them. Maybe we could break the ice and build trust with an exchange program between Russian and American intelligence outfits. We could could exchange assassination technology, an area were the Russians are 'cutting edge' at the moment..
Oh yeah, that's right, it's "illegal" for the US to order an assassination on a foreign head of state now. Sure.