Prime Ministers usually enjoy their visits to Washington. As the President is a head of state, his visitors receive quasi-regal treatment; you do not have to be Margaret Thatcher to relish all that. Gordon Brown used to insist that he did not enjoy such events, but that was in the days when they were reserved for Tony Blair. Since Mr Brown inherited the top job, he has become more appreciative of its perquisites.

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This is a good time for him to be in Washington. Mr Obama still seems to be on honeymoon with his electorate. Mr Brown will hope that some of the glamour rubs off on him. In advance, the Labour spinners have been working hard. We are told that the Brown/Obama meeting will be a progressive coalition against the forces of international conservatism. Every American leftist who was involved with the Obama campaign, however peripherally, will be wheeled out to conflate David Cameron and the Republicans who opposed the Obama fiscal measures.

This will not have much resonance, partly because it does not reflect the President's views. It is unlikely that Barack Obama is even aware of these manoeuvres. Around Christmas, there was a report that Mr Obama regarded David Cameron as "lightweight". This is believed to have originated with Peter Mandelson: not implausible. A member of Mr Cameron's staff contacted a core member of the Obama team who is now a senior figure in the White House. He e-mailed a one-word comment: "horse-shit".

Despite everything that the spin-doctors can do – and for this trip, nothing will be left undone – it is hard for foreign politicians to extract domestic political credit from dealings with the States. There is a recurrent problem. The Americans always have their own agenda, their own preoccupations. So the friendliest of allies can encounter difficulties in dealing with the best-disposed President.

That was even true in the great days of Reagan and Thatcher. Certainly, the background music was romantic. At gatherings of heads of government and foreign ministers, it is customary for the foreign minister to sit next to his boss. But Mr Reagan always moved the name-cards, so that he got to sit next to Maggie. It was a Hollywood love story – but as in all the best ones, the plot had complexities. The course of true love never did run smooth.

As is documented in John Nott's memoirs and John Campbell's life of Lady Thatcher, there were disagreements. On a number of occasions, the President was more favourable to the British position than some of his advisors would have liked. But Mrs T could never take him for granted. Still less could Churchill rely on Roosevelt's acquiescence.

Indeed, history may well conclude that it was Tony Blair who enjoyed the least troubled relationship that a modern Prime Minister has ever had with an American President. If so, there is a simple explanation. At various stages, Churchill and Thatcher both found it frustrating that the balance of forces condemned them to be the junior partner. But there was no reason for that to have troubled Tony Blair. He never wanted to express disagreement.

Geopolitics guarantees American superiority; geography reinforces American difference. It is easy for Europeans to forget that the US can look West as well as East and that Americans have concerns on their continent as well as in our one. Back in the Eighties, even when Maggie Thatcher was in her prime, Foreign Office ministers would express exasperation at the way in which the Americans would act first and consult later. It was ever thus.

When George Bush senior succeeded Ronald Reagan, he told his foreign affairs advisors that it was time for Margaret Thatcher to realise that she was not the leader of the Western alliance. He was. But this was not only perilously close to being ungallant. It was unnecessary. The public displays of deference by President Reagan may have irritated Vice-President Bush. In practice, they amounted to little more than a gentleman holding open the door for a lady.

There is a further reason why Gordon Brown's hopes for this week's visit greatly exceed Barack Obama's. Reagan and Thatcher: Bush two and Blair: in both cases, there was an incentive for the US politician to display his friendship with a British leader who was wildly popular in the States (much more so than at home). The same would have been true, no doubt, of Bush one if Mrs T had still been in office when he was running for re-election. But Mr Obama must now find it inconceivable that the day will ever come when he feels the need for electoral lustre from a British politician.

So despite all the fanfares and the grandeur, Gordon Brown goes to Washington as a supplicant, not an equal, and he suffers from a further disadvantage. He is not Margaret Thatcher or Tony Blair. Americans cannot be expected to take more than two British Prime Ministers to their hearts at any one time. Gordon Brown will address both Houses of Congress. He will, no doubt, make the speech of his life, which is not saying much. But the best that he can hope for is that by the end of the day, every American Congressman will know the name of Tony Blair's successor.

Mr Brown will be more concerned that the average British voter should conclude that the world is safer as a result of his efforts. This is improbable. Poor Mr Brown is gloomy enough already, so it is just as well that he cannot comprehend the degree of public scepticism which now confronts him. Even if he deserved one, he would find it hard to obtain a fair hearing. As he is undeserving, the matter does not arise. His attempt to pray Mr Obama in aid is a characteristic piece of intellectual dishonesty.

In the first place, the two men's approach is divergent. Mr Obama decided that the US needed a fiscal stimulus and has provided one at enormous cost, much of it expended on projects of doubtful value. Even if Mr Brown wanted to imitate this, he could not have done so, for which we should all be grateful. Had he tried, there would have been a gilt-buyers' strike, the value of the currency would have collapsed and the government would have been preparing for another visit to Washington: to the IMF.

The Prime Minister did produce his own fiscal stimulus: the cut in VAT, one of the largest tax cuts in British history, which was also one of the most irrelevant. It was based on a misdiagnosis. The British problem is not fiscal. It is monetary. There is plenty of cash around, but it is not circulating because the banks are not lending, causing a sharp contraction in the effective money supply.

The Tories have come up with a solution: a loan guarantee system, under which the Government would insure a large proportion of the banks' new commercial lending. The Government has vaguely promised a scheme of its own, but nothing has happened. Perhaps ministers were too busy negotiating Fred Goodwin's pension. Everything is drifting while Gordon Brown dithers over the detail.

The PM can now forget all that for a couple of days, while he enjoys himself. But he will not be flying home to a second honeymoon.