In principle they were very close — Gorbachev offered it up, on the condition that Reagan also dumped his Strategic Defense Initiative. Reagan liked the idea, except for that part — he wouldn't part with SDI. (He offered to share the technology with Gorbachev, who pointed out that the USA wouldn't even share agricultural technology with the USSR, how could he believe they would share a ballistic missile shield?) And that killed the deal.

In terms of actual realities, though, I wonder: could they have done it? I'm dubious. Reagan could cut arsenals by Executive Order, sure. But Congress could veto any formal agreements (treaties, which anyone who believed in "trust but verify" would have needed to put formal verification actions in place), and could, in theory, pass laws canceling quite a bit of an attempted roll-back. And I think they would have turned on Reagan on this markedly idealistic move. (The Democrats certainly would relish the possibility of being tougher on defense — they do always like those opportunities, given the way it is usually used against them by Republicans.) Reagan's advisors were, to say the least, completely against it, and worked actively to persuade Reagan to reject it.

And Gorbachev's position was even more tenuous. Yes, he was General Secretary of the Communist Party, the head honcho. But his power was not infinite — Stalin, he obviously wasn't. He wasn't even Khrushchev in terms of his toughness (and Khrushchev himself got deposed for less!). The military would have bucked him. They could have deposed him. He was already up against wall. (And let us not forget the hardliner coup attempt later on.)

Nukes are big business — big money, big power. They have political resonance all along the political hierarchy. Getting rid of them is the harder political activity — having them is the "easy" path, the one of least resistance. Were either Reagan or Gorbachev powerful enough to get rid of them, at the second height of the Cold War? In a world that would still have nuclear powers, in the face of both allies and enemies? As you can tell, I'm pretty dubious.

But still. If ever there was a moment when it seemed possible, it was at Reykjavik.

Further reading: David Hoffman's The Dead Hand is pretty great in terms of looking at both sides of this summit, the personalities involved, and the dangerous close calls that led up to it. Richard Rhodes' Arsenal of Folly is also quite good on this.