By Nick Assinder
Political correspondent, BBC News website
There is a complex puzzle gripping the attention of Labour MPs over the government's latest proposals to detain terror suspects for 42 days.
And it is simply this: "How on earth does Gordon Brown think he can win this one".
Mr Brown and Ms Smith are facing Commons battle
On the surface, the numbers simply do not stack up in either the Commons or the Lords.
Both the Liberal Democrats and the Tories are committed to opposing the new measures and one recent newspaper survey suggested there were 38 Labour backbenchers also ready to vote against it - with only 34 required to defeat the government.
Even if the bill gets as far as the Lords, things are no better for the government and an alliance of Lib Dem and Tory peers could kill it off.
At the same time there are no obvious signs that the government's reassurances, cajoling and even re-jigging of the proposals has had more than a minimal effect on its opponents.
As far as the opposition parties are concerned, there seems little advantage to them in getting Mr Brown off a hook of entirely his own making.
The Lib Dems are proud of their stand on civil liberties and believe they are echoing the public mood. There was never the slightest chance they would back off.
The Tories, understandably wary of being painted by Mr Brown as soft on terror, none the less believe that will not wash with voters who, they believe, can spot a bit of Labour game playing when they see it.
Shadow home secretary David Davis' line of attack is that the prime minister is, once again, using a hugely important issue for purely party political reasons.
Terror threat is said to be high
The Tories believe there are already contingency powers available to the government in the sort of emergency circumstances ministers are saying might require such an extension of detention powers.
Meanwhile, Labour rebels - who landed Tony Blair with his first Commons defeat when he tried to increase the detention limit to 90 days in 2005 - show little sign of crumbling.
A large number of those rebels are not up for negotiating over the number of extra days suspects can be held - 56, 42 or whatever - they simply do not believe there is a case for going beyond the current 28 days, which is already twice what it was before that 2005 vote.
Their case has been boosted by comments from the Commons home affairs committee, which found no evidence to support an extension.
The Director of Public Prosecutions Sir Ken MacDonald said he has not asked for the increase to 42 days and is "satisfied with the position as it stands at the moment" and former Attorney General Lord Goldsmith has also expressed severe doubts.
And there is a powerful lobby outside parliament also insisting such a move would be a fundamental assault on civil liberties and, in any case, would not work.
On the government's side, however, are police chiefs who say they need the powers in order to tackle increasingly complex terror cases.
And, it is argued, the government would be severely criticised if it failed to act and, as a result, allowed a major terror attack to go ahead.
Ms Smith declared: "We face a choice here. We can either sit on our hands, failing to recognise where there is a broad consensus that this is a risk that is growing and that we might well face in the future.
"We can risk having to legislate in an emergency in the future, we can risk, as some people believe we should do, having to declare a national emergency in order to be able to do it.
"Or we can legislate now - with the discussion that will be put in Parliament on the safeguards and on the circumstances in which it would be used - and have that available in the future," she said.
For many that is a powerful argument, particularly if it is accepted that intelligence does indeed suggest the level of threat is high and the complexity of investigations increasing.
That, however, is part of the problem - the government is seeking to legislate on something that "might" happen.
To win that sort of debate requires an unusually high hurdle of evidence to be jumped - and opponents do not yet appear to believe the government has cleared it.
This is only day one of the parliamentary debate and there is much positioning still to come, but at the moment, few can see how Mr Brown is planning to solve that original puzzle.