There is zero chance we want anything to do with Putin. He is still the same psychopath dictator that was despised by most of this country during the Bush era. He is essentially raping his country right now for his own personal gain, arresting or disappearing any and all opposition, he has suspended civil rights in the nation, and committed countless war crimes against several former Soviet states. And none of that includes what's going on in Syria right now. Putin is much closer to Stalin than he is to Gorbachev and getting into bed with him would be a fatal mistake.
Who did we get in bed with in the early 40's when we also had a common foe?
"The enemy of my enemy is my friend", it's more than a cute catch phrase.
Sometimes world affairs require us to hold our nose, and deal with the bigger threat.