I never understood why USA joining forces with Russia would be a bad thing for Americans. They are literally the only nation capable of kicking your ass, why not befriend them?
Because Politics. Bush Sr/Clinton and Boris Yeltsin all got along fine. Bush Jr/Obama and Vladimir Putin however are a much different set. Corruption and Nepotism is all bad and awful, but the single biggest driver of straining is the resurgence of a more aggressive Russia, with a government slowly slipping into a state of Totalitarianism. The fact that it has Nukes is just a bonus.
That being said Russia and the US already work together on a lot of things.
The most immediate would be the ISS and Near earth Space exploration.
Russia and the US worked together during the collapse of the Soviet Union in order to safeguard nuclear weapons and materials. Afterwards the US and Russia cooperate on the reduction of their Nuclear Stockpiles.
While opposing the Iraq war in 2003, Russia is a supporter of the War on Terror. It is active in helping the US patrol African coasts for pirates and lends support to US operations in Afghanistan and throughout central Asia. Both logistical and Military such as Spetznaz Operators working with JSOC and other forces(Intelligence and Geographical knowledge), training officers in those countries on Conter-narcotics and counter terrorism operations.
US and Russia also cooperate training wise. Operation Northern Eagle in Norway, Vigilant Eagle in Canada, and Joint Counter terrorist training in Germany between both.