When some Labour MPs question the Prime Minister's authority, therefore, what they mean is that they do not like his policy. And that they imagine that Brown would be a more left-wing leader - a hope that is surely destined to be disappointed. When Conservative and Liberal Democrat MPs question Blair's authority, they mean: "For goodness sake, when is it our turn?" And when journalists say his authority is draining away, they mean they are impatient to move on to the next big story.
As with David Blunkett's hasty return to the Cabinet six months ago, the issue is not the Prime Minister's authority but his judgement. Why did he adopt such a semi-heroic pose in defence of a policy that no Labour leader could have expected to get through the House of Commons? The early Blair, with the favourable media wind behind him, might have got this through with a majority of 179 or 167, but not with the current notional majority of 66. "It is better to lose and be right" is a noble-sounding cry, but it has not been the organising principle of New Labour for the past 11 years.
The only conclusion is that his judgement was wrong. But it is as well to be clear about exactly why. Too many journalists, including many that work for the BBC, take the view that simply by advocating the 90-day policy he demonstrated his unsuitability for any office higher than co-opted school governor. Much of the public debate is conducted on the basis that the proposal is so outlandish and draconian that Blair must have some complicated and sinister motive for putting it forward.
A more fair-minded observer might accept that there was a case for extending the 14-day limit. He or she might note that the detentions would apply to very few people (only 11 have been held for 13 or 14 days in the past two years), and would be reviewed every week. Such a person might also have noted that Lord Carlile, the independent reviewer of terrorist legislation, thought 90 days was a reasonable maximum, provided judicial supervision were strengthened - which it has been. As Charles Falconer, the Lord Chancellor, drily noted, "Lord Carlile is a Liberal Democrat, a QC and a lord, three groups of people that I've found are pretty sceptical about extensions of power for the police."
Lord Carlile said he knew of cases where, had the police been allowed to hold suspects for longer than 14 days, charges could have been brought. Our theoretical fair-minded observer might ask, however, whether it was absolutely necessary to go as far as 90 days. That theoretical observer turned out to be Michael Howard, who failed to rally the rather embarrassed Tory troops in his clash with Blair, but who won the argument by asking flatly for specific examples of when the 90-day provision would have made a difference. And then won the vote.
Blair's judgement was suspect because of the way in which he seemed to regard the issue as one of political positioning. At his news conference on Monday, his usually restrained prose was lit up by a startlingly vivid phrase. He attacked David Cameron and David Davis, who both want to be prime minister, for failing to back the police.
If he had adopted their position when he was running for the Labour leadership, he said, he would not have got away from any TV studio "without a little puddle of water being where I once was". It is not on the official Downing Street transcript because it was party-political, and so civil servants are not allowed to type the words. But because it was party-political, it seemed that he was simply adopting a pose in order to embarrass the Tories. Hence his final shot in the Commons yesterday, which was to ask the Conservative Party if they were really "where they wanted to be" on this issue.
Blair, of course, is perfectly capable of sounding simultaneously as if he is striking a pose and really believing in it.
His real error of judgement was not on the principle of longer detention, but on the absolutism with which he seized on the period of three months from the moment it was advanced, tentatively, by the police on 21 July. Charles Clarke, the Home Secretary, always regarded it as the basis of discussion, and always expected to compromise on a lower figure. He proved to be a better judge of the balance of argument between civil liberty and security - and of the balance of sentiment on the Labour back benches.
Curiously, from the point of view of those who say that Blair's judgement is becoming increasingly clouded by his impatience for a legacy, this has been a fault of the Prime Minister from the earliest days.
He has always over-reached himself rhetorically. His mistake this time was to insist that 90 days was absolutely vital. That put him in the strange position of distancing himself from the vote before it took place. "Do what you like," he seemed to be telling MPs. "At least it won't be my fault if something terrible happens."
And it puts him in an even stranger position now. Not because his authority is diminished, but because he has a smaller majority than he did. He has said that yesterday's outcome is second best, a "compromise with the nation's security". Yet he also said last night that if he made it an issue of confidence, "of course I'd win it".
If it is as important as he says it is, surely he has a "duty" to tell MPs to come back and vote again, knowing that the Government would fall if he lost. Only two explanations are possible. One is that 90 days really is not as important as all that. The other is that he cannot be sure that 34 Labour MPs would not use a confidence motion as a chance to get Gordon Brown in.
The writer is author of 'Tony Blair: Prime Minister', and chief political commentator for 'The Independent on Sunday'