Charles Clarke, the Home Secretary, was warned that the heavily-criticised proposal could be defeated in the House of Lords. To avert a bruising parliamentary battle, he also looks certain to retreat over the proposed detention of terror suspects without charge for up to three months.
Tony Blair made a passionate defence of the controversial package yesterday, dismissing accusations that it seriously undermined civil liberties. But Lord Morris, a former Attorney General under Mr Blair, predicted that judges and lawyers in the Lords would "examine it [the Bill] very carefully".
Lord Morris said of the proposed extension of the detention period from 14 to 90 days: "I think the police have to prove very carefully and to the satisfaction of legislators that this extension is needed."
Lord Ackner, a former law lord, added that the Government had gone too far in its plans for curbing freedom of speech. "I get the impression we are taking this too far, that there is a great risk that freedom of speech is going to be curtailed because of the breadth of some of the clauses," he said.
While there was a "prima facie case" for extending the length of detention under the existing terrorism laws, three months was too long, Lord Ackner said.
"With the ordinary custodial reduction it represents a six months' prison sentence. So this really raises the risk of producing a form of internment."
Lord Ackner said that if the proposal was to become law, then there must be a right of appeal to a circuit judge.
Ian Macdonald QC, a former special advocate cleared to hear secret service intelligence against foreign terror suspects, described proposals as crude and vague.
He said: "I'm not sure how you would square some of this with freedom of speech. If we don't enter a debate with some of these people [Muslim exremists], then how can we compete for their hearts and minds? What is needed is proper intelligence to defeat religious-inspired terrorism."
Kevin Martin, president of the Law Society, said he believed that the current law against incitement was already sufficiently broad.
He said: "In view of the already broad nature of incitement offences, we are unclear that a new offence of "glorification" would take the matter any further. We also think that it would be evidentially very complex."
Nor does the Law Society believe that the case is made out for extending detention from 14 days. Mr Martin said: "Powers to detain are already longer in terrorism cases. However, if there were to be any extension, it must be granted and reviewed by a High Court judge."
Mr Blair told Radio 4's Today programme: "Virtually every country in Europe, following terrorist acts, has been toughening up their legislation.
"And the fact that someone who comes into our country, and maybe seeks refuge here, the fact that we say if, when you are here, you want to stay here, play by the rules, play fair, don't start inciting people to go and kill other innocent people in Britain.
"I think that when people say this is an abrogation of our traditional civil liberties; I think it is possible to exaggerate that. I mean, as far as I know people have always accepted that with rights come responsibilities."
Within Downing Street there was irritation yesterday that a leaked early draft of a letter by Mr Clarke appeared to reveal his private reservations over the planned new detention period.
Following a report that he was to be replaced as Home Secretary, Mr Blair has assured him that his job is safe. But there are tensions between No 10 and the Home Office over the handling of the anti-terrorism legislation.
MPs were stunned when the Prime Minister chose 5 August, while Mr Clarke was on holiday, to announce fresh proposals to protect Britain from attack.
The Home Secretary has also been noticeably more emollient to judges than Mr Blair, although Whitehall officials insist suggestions that there is a division between them have been exaggerated. However, one civil liberties source insisted last night: "There's a turf war: it's going back and forth."