Their intention was to signal support for the peace process but, ironically, it appears they instead dealt a grievous blow to its chances of success.
Over the years that process has often looked doomed: one 1996 book by a respected academic has a whole chapter entitled "The end of the peace process", explaining how it died out that year. Yet still it moves, though the referendums to be held on Friday look likely to represent a setback rather than the momentum they were supposed to deliver. This is because a majority, or near-majority, of Unionists look poised to back the Rev Ian Paisley's No campaign.
The Good Friday agreement already represents an extraordinary achievement, winning as it has the endorsement of 95 per cent of nationalist Ireland, every British political party and of every involved international player, including Bill Clinton. Nobody likes all of it but all of them regard it as a fair and workable compromise.
The exception is Unionism, where the agreement has exposed a fracture in its ranks so fundamental that it may result in new party alignments. The main grouping, David Trimble's Ulster Unionist party, is clearly split from top to bottom, and so is the Protestant community in general.
One gloomy scenario compares Mr Trimble to Captain Terence O'Neill, the reformist Unionist leader of the 1960s who concluded that change was necessary but lacked the political skills and support to bring his followers along with him.
Irish nationalists were amazed, to the point of shock, when Mr Trimble signed up for the Good Friday accord, given his record of rejecting almost all such compromises in the past. Initial amazement turned to delight as he robustly stood by his decision, but now it is turning to dismay as his capacity to deliver is cast in doubt.
If the opinion polls are correct, and if no reversal of present trends takes place before Friday, it seems that more than half of Unionists will vote against the agreement. This stance is an informed one: the grass roots are attentively reading the papers and, especially, watching television programmes on the issues.
And the majority Unionist view, put with classic simplicity by a leader of the Orange Order, is: "We've looked at this agreement and we don't like it." In vain, it seems, have Mr Trimble, Tony Blair and President Clinton asked them to vote Yes; in vain has Gordon Brown visited Belfast distributing money. They just don't like it.
In vain, the Yes campaigners argue publicly that voting No means opting for the past rather than the possibility of a brighter future, and that No campaigners have advanced no feasible alternative. In vain, they argue, more privately, that a No vote would mean the world writing off Northern Ireland as an intractable problem unworthy of further attention.
The Government itself has opted for offering plenty of carrots but hiding the stick. The agreement's virtues are lauded, but Mr Blair has carefully avoided issuing even implicit threats about what a big No vote would mean.
If the question of prisoners was the only sticking-point something could be done to make the arrangements more palatable. But although it is the issue most highlighted by the Unionist critics, it is obvious that the opposition to the agreement goes much deeper.
A senior Protestant cleric said yesterday: "I haven't found one Presbyterian minister who is voting No, they will all be voting Yes. But a number of people in the congregations who were waverers saw the Balcombe Street gang on TV and said: `That's it, we're voting No.'"
There is an awful lot of bigotry about in Northern Ireland, and a good proportion of the No voters are not just anti-republican but frankly anti-Catholic. Then there are others who agonised about the decision but were swayed not by the Balcombe Street event itself but by what it symbolised: a whole new political dispensation, part of which is to be the entry of Gerry Adams into a new government.
More than half the Protestants are, it seems, not prepared to go out and vote for that, whatever political and financial resources the Government deploys to entice them. Most of them want peace, but not at this price; and some sound suspiciously more at ease with the old paradigm of conflict than with the prospect of change.
Voting No will automatically put them into the Paisley camp, and it is here that a possible meltdown scenario heaves into view. A vote of, say, 60:40 on Friday in favour of the agreement will technically provide the necessary endorsement for it, but would also make clear that a substantial majority of Unionists are opposed.
The battleground will then immediately switch to the elections to the assembly, which are to be held on 25 June. Mr Trimble is trying to ensure that his party selects pro-agreement candidates, but a strong No vote in the referendum will make him look like a loser and portray Mr Paisley as a winner.
At that point, the more nervous in the Unionist Yes camp may give up the battle, for this has certainly been the pattern in the past. Absolute disaster for the Government will come if a coalition of Paisley members and anti-Trimble Unionists make up more than 60 per cent of Unionists in the assembly, for, under the rules, they could block every vote and paralyse the agreement.
While that is the Government's nightmare, the chances are it will not be so bad. It seems inevitable, however, that a civil war is beginning within Unionism between those who want a deal and those who don't. The new assembly will be the scene for many bitter battles.
It could take years to resolve this internal strife, with no guarantee that the Trimble camp will ever triumph over their Paisleyite opponents. One Unionist Yes campaigner said mournfully yesterday: "From the Nos you get a focused, clear, direct, simple message - just say No. It's not like that for us, we have to make complicated arguments."
One astute nationalist commented: "The Unionist case for the agreement is hard to make because it's actually negative. It's hard for them to say to their people: `Look, this is the best we could get, if we don't accept this, it will only get worse for us.'"
The campaign thus goes into its final week with the Paisley No camp in the ascendant and their opponents fervently hoping for a dramatic reversal of fortune.
Once again, the peace process is in need of last-minute deliverance from those who wish it dead.