The bill, which will face a vote in the House of Commons on Wednesday, has provoked outrage from civil liberties groups and risks a revolt by Labour members that could hand Prime Minister Gordon Brown his first parliamentary defeat.
"This is about doing the right thing for the country," Smith told BBC television's Andrew Marr Show. "That is why I am asking people to support this on Wednesday."
It was the latest attempt by Brown's ministers and government managers to push through a change in legislation that they argue is crucial to combat a growing terrorist threat.
Defeat for Brown could critically damage his already waning authority after the loss of a formerly safe parliamentary seat, a near wipe-out in local elections, a sharp slowdown in the economy and an embarrassing U-turn on tax reform.
An ICM poll in the Sunday Telegraph showed Labour 16 points behind the main opposition Conservatives on 42 percent and only five points ahead of the third-placed Liberal Democrats on 21.
It said it was the lowest rating recorded for Labour in any ICM poll. Another poll last week said Brown's approval rating was the lowest for a Labour leader since World War Two.
But the same poll offered Brown a glimmer of hope, showing that 65 percent of people questioned supported the detention extension to 42 days and only 30 percent said it should stay as it is -- the position taken by the Conservatives.
On the other hand, it also showed that most people thought the Conservatives had the tougher anti-terrorism policies.
COMPLEX PLOTS
In a letter to all Labour parliamentarians on Saturday, Brown said the extension was vital, noting the growing complexity of plots facing the security services.
"In 1997, 19 mobile phones, one computer and seven computer disks were seized in terrorist investigations. In 2006, 1,620 mobile phones, 353 computers and 2,541 computer disks were seized," he wrote.
Investigations in 2004 into Dhiren Barot, the head of an al Qaeda plot to carry out bomb attacks in Britain, involved the seizure of 270 computers and 2,000 disks as well as inquiries in seven other countries, Brown noted.
Barot was jailed in November 2006 for a minimum of 30 years.
Brown, who took over from Tony Blair last June after a decade as his finance minister, wrote that British security services were investigating 2,000 terrorist suspects, 30 plots and 200 organised terrorist networks.
To try to win support from party members who fear that under Brown's leadership they will lose their seats in the next election, due within two years, he has offered parliamentary and legal oversight of individual cases.
Any decision to go beyond 28 days will have to be agreed by both the police and the director of public prosecutions, and the home secretary will have to make independent legal advice available to parliament.
A senior judge will have to approve individual detention cases every seven days and the power to hold a suspect beyond 28 days will only remain in force if both houses of parliament vote to maintain it.
