His thinking goes like this: first, a young generation had witnessed peace in Northern Ireland for the first time in their lives; second, it is time to look to the centre for a non-violent settlement of the Irish question.
In his Panorama interview on Monday, he urged the people of Northern Ireland: "Don't look to the extremes, don't turn in temptation to the voices of extremism, whether they are Protestant extremism or whether they are Catholic extremism. Turn to the centre, to the political leaders who are looking for a peaceful future."
If Sir Patrick Mayhew was a strong Secretary of State for Northern Ireland, he would tell the Prime Minister that he is talking balderdash. But he is not a strong Secretary of State.
In spite of official denials, Mayhew told Major last year that he would willingly step down if the Prime Minister felt that Michael Ancram, his deputy, would do a better job. Now we know that Mayhew is not standing at the next general election, and the most common assessment of his position, across the Commons, is that of the lame duck minister.
As the events of the past week have left the Government with a lame duck Irish policy, it is appropriate. We should have a lame duck to run it.
Major in his TV interview has repudiated any further hope of political rapprochement with either Sinn Fein or the loyalist fringe - leaving the stable door wide open for a return to full-scale violence. Yet on Monday he asked: "Do we want to return to the 25 years of murder, mayhem, slaughter, indiscriminate bombings ... Or is it my job, everyone's job, to try and get that put behind us forever?"
A strong Secretary of State might have pointed out to his Prime Minister that this was patent nonsense after the extremism of David Trimble had been so openly rewarded at Portadown when the police allowed an Orange march to proceed.
The Prime Minister and Mayhew say that the decision had nothing to do with them, and that the Chief Constable, Sir Hugh Annesley, dreamt it up all on his own. In fact - and it is a fact - Annesley had repeatedly been told by Her Majesty's Government that the march was unstoppable, and the sooner he let it go the better.
Major got his first job in government from Mayhew, when he became his Parliamentary Private Secretary in 1981. They get on exceedingly well and Mayhew is one of Major's staunchest allies. There have been moments when Mayhew's sheer unflappability has helped to carry the peace process through crisis. But the Secretary of State, an honourable man, has been turned into the Prime Minister's poodle.
Mayhew's public stiffness belies a private, personal charm that inspires strong support in other parts of the Tory party. One senior figure said this week that Mayhew should stay to keep out his deputy, Ancram, who was an "appeaser ... like all nobs". That was a reference not only to Ancram's aristocratic background, but to the view that he would have given way to the Orangemen days before Sir Patrick. Mayhew is a well-heeled toff by any measure, but Ancram is blue blood - by such yardsticks are men still measured in Tory circles.
Now the problem is that whoever sits in the seat - Mayhew is the 10th Secretary of State for Northern Ireland since 1972 - it will make little or no difference to the direction of government policy. Major is now clearly calling the shots and, equally clearly, he has tilted towards the Unionist cause.
Major believes that the Orange Lodge was wrong to seek to proceed in the way it did at Portadown, but he also believes that the local Catholic community was "unreasonable in the way they refused to ... compromise for a long time on how a peaceful march could have been passed through the Garvaghy Road estate".
If the Prime Minister could have seen the grief and outrage on the faces of nationalist SDLP MPs on the day that the march was allowed through, he might perhaps have put that differently. Yet he is confident that those same SDLP MPs will be striking deals with David Trimble, saying: "The SDLP have been foremost in recent years in talking about the importance of dialogue". They were also foremost in urging the inclusion of Sinn Fein, who now seem to have been shut out.
If Sir Patrick was the organ grinder in this operation, he might be credited with a remarkable achievement; uniting the right-wing Unionist tradition of the Conservative Party and the nationalist community of Northern Ireland against him.
There was strong speculation among the Tory backwoodsmen on Monday night that Sir Patrick's days might, after all, be numbered. In spite of the strongest guidance to the contrary - Number 10's statement that there was going to be no change of Cabinet in this month's expected reshuffle - there were strong suggestions that Sir Patrick might go anyway. The pity is that his epitaph could now read: "It did not matter if he went, it did not matter if he stayed."
Major should have let him go last year, and let him go with the dignity that was left. Now the policy is in tatters and Mayhew is the fall guy.