From a DoD fact sheet (linked in reference).
What you see: shortly after the Cuban Missile Crisis convinces us we need a new model, the MAD (mutually-assured destruction) paradigm allows us to start tapering off and then reverse our astronomical climb. Arms control treaties across the 1970s and 80s reduce it a bit more, while slowing the USSR's phenomenal climb. Then big drop at end of Cold War, plateau until mid-200s, and then another significant fall.
Point: notion that we have too many nukes or haven't done enough to cut numbers is wrong. We have less than 15% of the warhead total we had at the Cold War's scary peak in the early 1960s, meaning an 85% decline.
Why Obama thinks this is the big issue of our day is beyond me, as is the notion that we should reduce the role of nukes to somehow convince Iran not to reach for them.