Even so, he is determined to carry on trying. How can he make it a little likelier that he will succeed? Given the imminent approach of spring, some of the gossip round Tory Whitehall is about whether he will use a summer reshuffle to reconstruct his government dramatically. This is all very well - except that the scope for any likely reshuffle seems limited.
Tory traditionalists talk about 'drafting Douglas' and 'drafting Hezza'. But despite persistent press rumours and advice, Douglas Hurd has not decided to quit as Foreign Secretary. He is motivated by a mixture of party loyalty and concern about his possible successor - these are not easy times Abroad. Although he could do with a higher income - he has little money of his own and a young family - he is not naturally attracted to jetting the world on behalf of a merchant bank, rather than Her Majesty's Government. He takes a close interest in domestic politics and can be credited for Christopher Meyer's appointment as Number 10's press officer. But that does not mean he is now ready to act as wrinkled retainer to Mr Major.
Kenneth Clarke, another key player, is working on the assumption that he will be Chancellor of the Exchequer until the next election. He is an obvious candidate for the Foreign Secretaryship in due course, if Mr Major stays on. It would offend that section of the Conservative Party which reads the Sunday Telegraph. But the rest of us might welcome a self-confident Europhile in charge of overseas policy. Before that, however, Mr Clarke has some tax-cutting to do.
What then of the Shere Khan of Tory politics, Michael Heseltine? Since becoming President of the Board of Trade he has pursued a programme of quiet reform of his department's structure and effectiveness, apart from dealing with the unpopular coal closures. Since his heart attack he has been still quieter, though recent radio and television interviews have shown a return to something like the old form. There is a glint in the eye, the occasional ominous tail-flicker.
Some supporters of Mr Major would dearly love Mr Heseltine to take over from Norman Fowler as party chairman. Conservative morale is likely to be so low after this year's elections that the arrival of Heseltine red in tooth and claw would cheer even even the grass- roots Thatcherites. But so far, this prospect does not seem to have much tempted Mr President.
So although a 'committee to re- elect the Prime Minister', featuring Messrs Hurd, Clarke and Heseltine, would be the sort of dramatic refocusing of the Government which voters might notice, it seems unlikely to happen. That being so, no reshuffle is going to help Mr Major that much. True, he could chuck out a few right-wingers, as he is being urged to do. But such muscular displays, however gratifying to the Westminster villagers, are unlikely to be thorough enough to change the whole tone of the administration, thus making the country sit up and pay attention. For instance, John Redwood, the Welsh Secretary, is a popular candidate for chucking out among those who want to defenestrate Michael Portillo but cannot bring themselves to suggest it. Hmm. Would they really notice that in the Rover's Return?
Another current suggestion for Cabinet reform is more to the point - that the Number 10 machine should be expanded into a full Prime Minister's department with its own cabinet minister. Compared to other national leaders, Mr Major is ridiculously under-resourced in terms of thinkers and strategists: a seven-strong policy unit, which spends most of its time on damage limitation, and a single political adviser, is a small personal retinue. There are various committees of advisers and ministers and whips, and the occasional 'political cabinet meeting'. But Mr Major's own staff is tiny. Small wonder that he has to spend so much time, in the words of one official, 'responding to other people's agendas in a truculently defensive way'.
A PM's department would be able to deal with Mr Major's current initiatives, such as the Citizen's Charter and the open government programme, but with the personal authority of the Prime Minister. It would be able to do better long-term planning than the rather ramshackle, overworked Downing Street machine can at present. And, with a minister working directly to him, the Prime Minister would have to cope with less of the daily burden of instant explanation and reaction. The ridiculous job would become less so. Imagine, there might even be the odd moment for reflection and serious thought]
This isn't a wholly new proposal. But the idea is now being widely discussed by Concerned of Whitehall and senior Tories at Westminster. Indeed, a similar plan has been put to Mr Major. The word is that he reacted coolly. Why? Perhaps he dreaded headlines like 'Whitehall tries to shore up Major'. Perhaps it was the old macho problem of not wanting to admit that he needs more help out there on the ice.
But a good idea that could help restore the diminished office of Prime Minister, and which would be a useful reform in itself, should not be discarded out of amour propre. Mr Major should take time out to consider it properly. Otherwise, I fear . . . thud, thud, THUD?