Britain already has some of the toughest anti-terrorist laws in the world.
The police can hold someone suspected of a terrorist offence for two weeks before charging or releasing them - so why does the government want to extend that period to three months?
Mr Clarke has backed three-month detentions for terror suspects
The answer, according to the Home Office, is that the nature of the terrorist threat is unique.
Police can't afford to wait until all the usual criteria of evidence are met.
They have to intervene swiftly to stop any suspected terrorist activity.
Only then can they start to build a case - and this takes time.
Also, a lot of the intelligence currently used against terrorist suspects comes in the form of encrypted computer data that is complicated to unravel.
Plus, the sheer volume of evidence gathered in some of the most high-profile cases means it's difficult to build a convincing case in as little as two weeks.
So the government wants the option of holding people for longer, subject to weekly reviews by a judge.
But the proposal has horrified the civil liberties group Liberty, which has called it "a new British internment". And the main opposition parties are worried too.
Will people in the UK who express support for, say, the Palestinians or the Chechen rebels, be hunted down by anti-terrorist police?
It is likely to be one of the biggest stumbling blocks to securing cross-party support for the raft of proposals.
But some of the other proposals are also likely to prove controversial.
As well as creating an offence of encouraging terrorism, the government also want to outlaw publications that "glorify" terrorism.
Distributing such material would be illegal too, raising the possibility of police raids on Islamic bookshops.
Critics say this is an unacceptable restriction of free speech.
Will people in the UK who express support for, say the Palestinians or the Chechen rebels, be hunted down by anti-terrorist police?
And how much would this help defeat the kind of terrorists responsible for the London bombings in July? Will it simply drive radicals underground where they are harder to monitor?
Other aspects of today's draft laws, though, are likely to find more support.
Few will argue with the authorities when they say the ruthlessness of suicide bombers justifies long prison sentences for anyone involved in the preparation of acts of terrorism at whatever level.
Many Muslim leaders are already concerned about young men from their communities attending terrorist training camps.
But the broader question of the balance between civil liberties and the security of the state will be rigorously debated.
The prime minister said the events of 7 July changed the rules of the game.
But his critics warn that an unnecessarily illiberal response could act as a recruiting sergeant for extremists.
And they remain to be convinced that all of today's proposals will really help defeat terrorism.
Meanwhile, a series of police raids in London and Manchester today is likely to lead to a test of other security measures.
For some time ministers have been trying to draw up agreements with various north African and Middle Eastern countries that anyone deported there would not face torture or execution.
All seven of the men detained today for reasons of national security are Algerian and their lawyers are likely to argue that sending them back to a country with such a poor human rights record would be illegal.