Unionists want a weak government reliant on Unionist support in the Commons; nationalists want a stronger administration with no need of Unionist assistance.
But the possibility of a Labour government means that Irish politicians are already flicking back through their legendarily compendious memory banks for indications on how a Blair-led government might perform. Labour policy on Ireland has see-sawed wildly over the decades, going through nationalist periods but also decidedly Unionist phases. In many ways it is a tale of radical instincts curbed by the exigencies of office.
There has been much change since Labour was last in power, but the fact is that many of the same factors and forces, and indeed some of the personalities, will be faced by Tony Blair and Marjorie Mowlam, who, everyone assumes, will be his Northern Ireland Secretary. New Labour will have to face the old Irish questions.
Mowlam has held the Northern Ireland brief for many years, but Blair has shown only the most perfunctory interest in Ireland. Their party has, though, gone through the same painful learning curve as everyone else in these islands, which means they will not approach the problems, as some of their predecessors did, in a state of almost complete ignorance.
The first occasion when a Labour government ever really came to grips with Ireland was almost half a century ago, in an episode which, though now part of history, offers a telling insight into the party's perspectives.
In 1949 the Dublin government unexpectedly announced that Ireland, though effectively independent for many years, would formally declare a republic and leave the Commonwealth. This huge constitutional change meant that the Attlee government needed new legislation to regularise Northern Ireland's position.
Up to that point the Labour government had exhibited what one of its junior ministers, the pro-nationalist Lord Longford, described as "a rather hazy benevolence" towards southern Ireland. This was very much a traditional Labour approach, for expatriate Irishmen and their descendants had played a significant role in the movement since its early days.
When it came to brass tacks, however, such sentiment went by the board. The government inserted a clause in the new bill laying down that Northern Ireland would remain in the UK so long as a majority in the Stormont parliament in Belfast wanted it.
Since Stormont had an inbuilt Unionist majority, nationalists protested that the clause ensured the partition of Ireland. But Attlee's Cabinet tended to lean towards the Unionists, largely because his deputy, Herbert Morrison, had been much impressed by the Stormont prime minister, Lord Brookeborough, and by Northern Ireland's role in the Second World War. Conversely, he and other ministers had been unimpressed by the South's wartime neutrality.
Against this background the Cabinet made its hard political judgements. The first of these concerned the reality of Protestant power, and a desire to avoid stirring up Protestant anger. The Cabinet discussed the 1912 period, when Unionists had armed themselves with German guns, forming the Ulster Volunteers and declaring themselves ready to use force to resist home rule.
The 1949 Cabinet minutes record Labour's conclusion: "Unless the people of Northern Ireland felt reasonably assured of the support of the people of this country, there might be a revival of the Ulster Volunteers and of other bodies intending to meet any threat of force by force; and this would bring nearer the danger of an outbreak of violence in Ireland."
The second issue was closer to home: that of the UK's wider strategic defence considerations. These were set out by the Cabinet secretary, Lord Normanbrook, who wrote that the South's move meant that keeping Northern Ireland within the UK had become "a matter of first-class strategic importance to this country". The issue was so vital, he argued, that even if Northern Ireland wanted to leave the UK it was unlikely any British government could allow it do to so.
The new bill in effect formulated a principle which is still a matter of everyday political argument: that Irish unity can only come about with the consent of a majority in Northern Ireland. What went by the board in 1949 was the issue which came back to haunt these islands 20 years later: the question of the fairness of the Stormont system.
When Longford protested that Catholics were being discriminated against he was heard out by the Cabinet, he recalls, with "chilly indifference". The young Michael Foot supported the bill but went on to call for a commission of inquiry into Stormont's "monstrously undemocratic methods."
But the minutes show that the Cabinet decided to keep its distance: "It was the general view of ministers that the UK government would be ill- advised to appear to be interesting themselves in this matter." Exactly two decades later, another Labour administration was in power when the civil rights issue spilled over into the streets and into violence.
In the Sixties and Seventies, governments headed by Harold Wilson twice considered the idea of aiming for a united Ireland. They decided against such a course: and in doing so they demonstrated the continuity of the Irish issue, for they were influenced by much the same factors as the Attlee administration had been.
But Wilson, unlike Attlee, took a much closer interest in the issue of civil rights for Catholics. He supported and encouraged the reformist policies of the then Unionist prime minister, Terence O'Neill, expressing open hostility towards opponents of reform such as William Craig (an early mentor of present Unionist leader David Trimble) and the Rev Ian Paisley.
Wilson himself came under pressure to intervene more directly from a large number of Labour MPs, many of whom, such as Kevin McNamara, had Irish backgrounds and sympathies. Wilson was conscious of the large Irish presence in his own Liverpool constituency, remarking often that he had more Irish voters in his constituency than had many Dublin politicians.
His own instincts were radical, and the idea of pulling out of Northern Ireland was secretly considered, though rejected, before the August 1969 eruption of violence and deployment of British troops. Wilson was fully prepared to scrap Stormont if the Unionists did not hand over many of their security powers, but they agreed and their institution survived.
While the issue of civil rights assumed a new importance in 1969, some points remained practically unaltered by the passage of time. Like the Attlee Cabinet, Wilson's ministers worried about a revival of the Ulster Volunteers. According to Tony Benn's diaries, Defence Secretary Denis Healey warned the Cabinet that "although he had sympathy with the Catholics, he had to point out that if we had the majority of the population against us we should be once again in the 1911-14 situation."
Britain's strategic military interests also remained a consideration. One of Wilson's aides noted later: "There were and still are arguments for Britain not pulling out of Ireland. However, the only positive reason for staying in which really mattered in Whitehall was defence."
In opposition in the early 1970s, Wilson appalled Unionists. First, he openly espoused the aim of Irish unity; second, he secretly met the IRA at least twice, infuriating not only Unionists but also the Irish government, which took the view that he was, in effect, encouraging terrorists and undermining democratic politicians.
Unionists were therefore apprehensive when he returned to power in 1974. They were right to worry, since in strictest secrecy he established a Cabinet Office committee to review options which included British withdrawal and independence.
But within months the Unionists inflicted a decisive defeat on his government's authority by staging a general strike which brought down the power-sharing executive of the time. When Wilson referred to loyalists as "spongers", they responded by defiantly sporting pieces of sponge on their lapels.
Many, including Wilson, saw the success of the strike as the clearest possible indication of the Unionists' strength of numbers. It was, in effect, a stark demonstration of the Protestant power to which Attlee and Healey had accorded such wary respect.
His sights lowered from the aspirational to the managerial, Wilson and his hapless Northern Ireland Secretary, Merlyn Rees, afterwards presided over a policy still remembered for its confusion and lack of direction. Political talks got nowhere, and nor did further contacts with republicans. Amid the uncertainty the death toll rose.
Amid the confusion, Dublin minister Garret FitzGerald, worried that Wilson might opt for British withdrawal, lobbied Henry Kissinger, then US Secretary of State. He told Kissinger that Dublin might seek American assistance "in persuading Britain not to embark on a course of action that could be so fraught with dangers".
FitzGerald's fears, as he later acknowledged, were groundless. Far from pursuing Irish unity, the Callaghan administration of 1976-79 executed a dramatic change, transforming itself from the one-time champion of Catholic rights into, at least temporarily, the sponsor of Unionist interests.
Roy Mason, as Northern Ireland Secretary, revelled in the pro-consular trappings of the office, eschewing political initiatives in favour of a hardline security policy. This involved extensive use of the SAS and police interrogation methods which earned condemnation from Amnesty International and others.
This approach was so popular with Unionists that years later the mention of Mason's name could still draw applause from an Ulster Unionist party audience.
The tough security policy was accompanied by concessions to Unionism at Westminster, where Callaghan's minority government needed Ulster Unionist support in the lobbies. That period is remembered - as these last days of the Major government will doubtless be - as one in which a prime minister put the survival of his administration above other considerations.
Callaghan paid the price, however, when his policies led the then leader of the SDLP, Gerry Fitt, to vote with the Conservatives in a no-confidence motion. "Labour policy since 1974 has been disastrous," Fitt said in an emotional, still-remembered Commons speech. "The Government has disregarded the minority and appeased the blackmailers of the Unionist majority." Fitt's vote - the first he cast against Labour in 14 years - helped bring down the last Labour government.
Out of office, Labour at first reverted to a more pro-nationalist line, in the early Eighties adopting a policy of pursuing Irish unity with Unionist consent. In the past few years, however, Blair has significantly softened this approach.
He first removed Kevin McNamara, the shadow Northern Ireland spokesman who was identified with "old Labour" and known as a passionate Irish nationalist. His replacement, Marjorie Mowlam, and Blair himself have since made it clear that while the party is still technically committed to unity by consent it will not push Unionists in that direction.
They will none the less place a high priority on an Anglo-Irish approach, involving the South in the administration of the North, and increasing London-Dublin co-operation. The Irish vote may no longer be a factor of note in British politics, but it has been replaced with the much stronger influence wielded today by Dublin.
This mild greenery is derived not so much from Labour's own instincts as from the general consensus (with the significant exception of the Unionists) that the political facts of life are Anglo-Irish. But many of the issues faced by his Labour predecessors will still be there. The defence issue may have dimmed, but the issue of the integrity of the UK will be on the Conservative agenda, and therefore on Labour's also.
And while the South's influence has grown, the reality of Unionism's strength of numbers is still evident. Only a few months ago the Drumcree episode, which amounted to a minor key rerun of the 1974 loyalist strike, provided a salutary reminder of the realpolitik of potential Protestant power.
Blair would bring to the post no strong instincts on Ireland, though his general approach suggests he would not favour any Wilson-style adventurism. His policies may be further circumscribed by the Tories, who in opposition might well opt for a stronger pro-union line.
But the most important determinant of Labour's approach, as it threads its way through the Irish minefield, may well be the size of its majority. A strong Blair government will have a tricky enough task in working towards peace and agreement; but a weak administration, dependent on Unionist support in the lobbies, would be something close to a nightmare for nationalists, and indeed for Blair himself.