Sure it was a huge generalisation and seemed to ignore the efforts being made by David Trimble and Gerry Adams, among others. But if I understood Mr Clinton correctly he was saying that they could talk and talk but seemed unable to make the final leap. There was always something which seemed to pull them back to where they'd been before, a kind of addiction to the certitudes of tribal politics.
With the Ulster Unionists assembly members saying No to the latest peace proposals, we seem to have confirmation that Bill Clinton was right. Here is a deal recommended by their own leader, a chance to get a power-sharing government up and running for the first time in Ulster's history and what do they do? Say No to make it impossible for Mr Trimble to move forward. Years of negotiations have apparently foundered as Mr Trimble's assembly party splits down the middle.
The deal which is being offered is not "guns for government", as they might have wished for at the outset of the negotiations. But have the Unionist opponents of the deal forgotten that these are "negotiations". They are about that still unfamiliar concept in Ulster - give and take. And what Mr Trimble has managed to extract from the republican side is considerable, the nearest thing to the decommissioning of weapons that can be achieved.
The impasse over decommissioning was never going to be resolved by a clear victory for either side. It was too sensitive, it went too close to the core of the Unionist sense of grievance and the militant republican sense of identity for any easy resolution. And so what we have now is the blueprint for a "process". I believe that the process will deliver gradual decommissioning. But the best guarantee of a prolonged peace is the power-sharing executive in which all sections of the community have a say.
If Mr Trimble deserves credit, so too do Gerry Adams and Martin McGuinness who have brought the hardliners in the IRA to the point of declaring that the war is over and, apparently, a willingness to appoint an interlocutor to deal with the weapons decommissioning body. This is not about patting the IRA on the back for being kind enough to stop killing people. But we should be able to recognise that bringing the gunmen to the point of accepting unemployment is a singular feat.
But none of this has been good enough for a substantial proportion of Ulster Unionists. There are some of them for whom any deal with the IRA is anathema. There are doubtless some for whom the idea of sharing power with any Catholics is an unlovely prospect. As Mr Clinton correctly suggested, the atavistic addiction still retains a disturbing power. Mr Trimble has said he is worried not by the quantity of the opposition but by its quality. For this read Mr John Taylor, his deputy and one of the longest serving Unionist politicians in the province. I had always taken Mr Taylor to be a pragmatic political operator rather than an absolutist. True he understands the reality of republican violence having been shot by the Official IRA in the Seventies. But he stayed by Mr Trimble's side for a long time in these negotiations before finally declaring with the nay- sayers.
But would John Taylor or any other Unionist leader be able to secure a better deal from the IRA? I very much doubt it. What we need to hear now is how Mr Taylor and the other opponents of the deal plan to move the peace process forward. Because we are talking about political responsibility here. If you say No in a place like Ulster you have an obligation to advance an alternative route forward.
It is hard to imagine what Peter Mandelson could do now to coax the Unionist opponents of the deal to the table. Having made his case to the Assembly party the other day there is, presumably, little left to say. It is down now to the Ulster politicians, or rather those who oppose this latest deal. When they consider their next move they should remember that the Good Friday agreement - peace and power-sharing - is what the majority of people voted for. That is the mandate within which all the politicians must work.
It is easy to be depressed this morning. After writing that previous line I remembered how many times I'd written it in the past about Ulster. How often has the province been "in crisis" or "on the edge" or "facing a last chance for peace". A colleague of mine is fond of saying that the current peace process is "the only show in town". In other words, there is no alternative to talking and solving. He is right up to a point. Sooner or later there must be a power-sharing executive. It is what happens in the meantime that worries me.
It's not that I believe a collapse in the IRA ceasefire is imminent (in any case ceasefires don't collapse, they are cynically ended by gunmen and bombers). It is rather that the extremists who lurk on the edge of Ulster politics will gain more support. I doubt that it will ever be enough to destroy the process, but enough to destroy more innocent lives. The return of sectarian murder and the bully-boy rule of the kneecappers is a frightening possibility.
But in the past few weeks something has been happening which defies the ancient laws that govern Ulster politics. It is a change more fundamental than any in the peace process so far. While we have waited for the result of the talks we have overlooked the extraordinary dynamic which has propelled them to this stage in just a few weeks. The leader of the Ulster Unionists and the leaders of Irish republicanism have been talking... and trusting.
They have moved from mutual loathing to the point of agreeing a process. If you read this in mainland Britain its possible to miss the huge import of this. But David Trimble and Gerry Adams actually trusting each other. That is the kind of relationship on which lasting peace is built. I hope that Mr Trimble stays with the fight for peace. Having been rejected by his party he may well feel tempted to resign. This would be a tragedy for unionism and for Ulster. He may not always have been the wisest of leaders but he has learned fast.
The true measure of leadership is not cunning or ruthlessness. They are simply weapons, not a purpose. Too often in Northern Ireland we have been seduced by the hard man who refuses to give an inch. The fire-breathing puritan, the slogan-speaking revolutionary, surely we've had enough of that. Leadership in the style of David Trimble is about having the courage to risk your own future. It is about looking back down the years and seeing the waste and wreckage and pain and realising that by risking yourself you might just make the crucial difference.
David Trimble would make a good, maybe even a great First Minister of Northern Ireland in a power-sharing administration. I hope he gets the chance.
The writer is a BBC Special CorrespondentReuse content