They want Sinn Fein banished. This is partly because of the IRA's apparent return to killing, but more fundamentally because few if any Unionist politicians can conceive of a new settlement which might include republicans. Born and brought up in a state that regarded republicanism as the implacable enemy within, they found it impossible to envisage any other way.
The peace process, emerging as it did from Irish nationalism and gaining the endorsement of the Labour government, is based in large part on an abandonment of the traditional politics of exclusion. The argument is that both Unionism and republicanism might, for the first time ever, be accommodated in a new system. Mainstream Unionism never subscribed to this idea, taking part in talks only under protest and under sustained pressure from Tony Blair and Mo Mowlam. If Sinn Fein are this week expelled from those talks, there will be private celebrations among Unionist politicians.
As this analysis suggests, the two killings ascribed to the IRA have come as a body blow to Sinn Fein leaders, such as Gerry Adams, who have invested substantial amounts of political capital in working for entry to talks. They will now argue that the evidence of IRA involvement is not strong enough, the RUC's word should not be taken on this point, and that Sinn Fein's 17 per cent vote in Northern Ireland has given the party its own independent mandate.
But such arguments are unlikely to prevail. Last week's IRA statement asserting that its ceasefire was intact amounted to a classic "non-denial denial" of responsibility for the two killings. In the face of this studied ambiguity, the RUC's accusation of its involvement will carry much more weight and there is thus a real possibility that the republicans will be put out of the talks.
Those talks are scheduled to come to a conclusion in the month of May, which means that even a temporary suspension would remove Sinn Fein from the conference table during a crucial period. This would put paid to the cherished republican hope of achieving one-on-one meetings between Mr Adams and Mr Trimble. The concept of an inclusive settlement would thus receive a huge setback.
In political terms the killings made no sense at all, endangering as they have Sinn Fein's place at the table and thus the entire peace process. One of those killed, Robert Dougan, was a member of the paramilitary Ulster Defence Association who, it is said, dabbled in drugs. Both republicans and security sources say the other victim, Brendan Campbell, was a leading drug dealer. Some months ago he had launched an amazing one-man attack on Sinn Fein offices in Belfast with a machine gun and a hand-grenade. Although this was clearly an extraordinary challenge to the authority of the Republican movement, both men were essentially unimportant in the greater scheme of things. Their murders seem to show that, at this moment at least, the IRA is being driven not by the logic of politics but by the logic of the street and the ghetto. Killings of drug dealers are popular among many in republican areas.
So too, at certain times, are killings of Loyalist paramilitants. Last year saw Loyalists killing more than a dozen Catholics, a steady drip of death which, in recent weeks, escalated into a spate that left eight Catholic men dead within a one-month period. The IRA's guns remained silent during all this, the requirements of the peace process apparently dictating inactivity. But then something snapped, as a grassroots clamour for vengeance reached a pitch that could not be ignored. The low politics of the tribal imperative for revenge evidently asserted themselves over higher political considerations, and two men died.
All this has brought Sinn Fein to the point of exclusion, though the party will today attempt to mount a strong rearguard action, possibly including a legal challenge against any such move. The British and Irish governments will not want them to go but may feel there is no alternative. A surprising number of talks participants have privately come to believe in the bona fides of Gerry Adams and Martin McGuinness and do not think that they approved of these killings. But both are leaders of the republican movement and unless some startling new information comes to light today, the governments may well conclude that Sinn Fein cannot be at the table while the IRA kills people.
Expulsion carries huge risks. IRA violence could escalate, and if it does Loyalist retaliation would probably not be far behind. The recent deaths have already shown that a spate of a dozen killings can endanger the talks; another bout of serious violence might wreck the whole exercise. But if Sinn Fein are somehow permitted to stay, this could itself destabilise the talks. David Trimble has refrained from stipulating that if republicans stay he will go, but if they are not expelled he would certainly come under increased pressure to walk away.
It has to be remembered that two of the other Unionist parties, including the Reverend Ian Paisley's Democratic Unionists, have already walked out because of the very presence of Sinn Fein. Four of Mr Trimble's 10 MPs have already said they favour withdrawal, while important members of his negotiating team have publicly voiced doubts about the exercise. It is in fact arguable that, as things stand, only around half of the Unionist community is actually represented in the talks. On top of all this is the daily danger of more violence, either from groups who are in the peace process or from those small but active organisations, such as the Loyalist Volunteer Force, who are outside and intent on wrecking it. Add all these hazards together and many observers will wonder how the whole thing can possibly survive.
Yet it has weathered similar turbulence in the past, confounding everyone by its resilience. At this moment it is hard to see exactly how the republican instinct to stay in can be reconciled with the Unionist urge to push them out. All that can be said is that in the past difficulties have been overcome by the sheer determination of important figures involved not to give up. Such determination will be needed again to navigate successfully through the coming week of crisis and controversy.