If in 2010 the big nuclear weapons powers and UN Security Council permanent members - the United States, Russia, China, Britain and France - don't make significant reductions with their nuclear weapons then an important opportunity will be lost. US President Barack Obama and Russian President Dmitry Medvedev appear to be of a mind on this.
One has to go back to the US presidencies of John F. Kennedy and Lyndon Johnson to get the full picture on the dismal progress on nuclear disarmament. Their defence secretary, Robert McNamara, told both presidents nuclear weapons were unusable.
Henry Kissinger, when national security adviser to president Richard Nixon, publicly said the same, chiding the Europeans for thinking that they were under an American umbrella. He told them bluntly that America would never sacrifice its own cities to avenge European ones.
Later, president Ronald Reagan was quite clear that he could never push the nuclear button and that all nuclear weapons must be quickly abolished. He came close to striking a deal with the Soviet president, Mikhail Gorbachev, (another leader who said he could never push the button) at their summit in Reykjavik were it not for Russian intransigence in refusing to lift their objection to testing missile defences in the laboratory. Reagan's worry was that if he didn't get that concession, the right wing would eat him alive and he would not be able to get such a treaty through Congress.
In recent years, not only was McNamara on the warpath on behalf of radical disarmament, so have been the former bastion of the nuclear weapons' establishment, Paul Nitze, who was the chief negotiator on the old Strategic Arms Reduction Treaties (Start), Kissinger himself and a long list of former military commanders and political figures, both left and right.
Former president Bill Clinton must suffer much of the blame for slowing disarmament talks to a snail's pace. It was an unforgivable sin. Here was a president who inherited the peace brought about by presidents George H.W. Bush and Boris Yeltsin and yet put it on the shelf for want of drive, even interest.
President George W. Bush quickly struck a handsome deal with then president Vladimir Putin to shelve more than 1,000 big rockets and their warheads in storage.
It took a lot of the most dangerous weapons off instant alert - an intolerable practice that still continues for reasons few understand - and it was done very quickly within months without the need for a laboriously negotiated treaty that would have to be slowly approved by both parliaments.
It is, in fact, the template for what should be done now. Once the present negations are wrapped up on renewing and extending quite dramatically the cuts under the 1991 Start, the two leaders should meet and decide to put the rest of their nuclear missiles on the shelf. They should initially keep 100 or so out of the roughly 6,000 that used to exist in order to persuade Britain, France, China, India, Pakistan, North Korea and Israel to join the bandwagon. All of them would find themselves - including North Korea - under irresistible pressure to disarm.
In the 'in-club' there is much talk these days of taking a step at a time - for example, to get the Comprehensive Test Ban Treaty agreed on, a cause that has been on the table since Kennedy embraced it. Under Clinton, it did come before Congress for ratification, but Clinton made no big effort to get it through.
Another favourite is to work on the reduction of the smaller and simpler tactical (or battlefield) nuclear weapons, dangerously under the control of field commanders and often improperly stored in Russia. In some cases they have been found protected by a single barbed wire fence.
Then there is the campaign to hold both powers to a 'no first use' pledge, a load of codswallop if there was real tension and life-or-death issues at stake.
Obama is temperamentally tuned to taking big leaps that ignore the conventional wisdom. A reading of his Nobel Prize winning speech with his accent on 'love' between nations is path breaking. Medvedev comes across as a principled and idealistic man. His mentor, Prime Minister Putin, shows no sign he would want to hold him back on this issue.
Someone has to start the ball rolling. Best if they hold hands and do it together.
Jonathan Power is a London-based journalist