Ministers have said they are confident of overcoming a possible Labour rebellion over plans to replace the UK's nuclear weapons system.
The government could be forced to rely on Conservative votes
A total of 64 out of 101 Labour backbenchers who responded to a BBC survey said they opposed renewal.
MPs will vote on Wednesday on a £20bn government plan to replace the Clyde-based Trident system.
Defence Secretary Des Browne said he was "confident" MPs would be persuaded to agree with the government.
Lack of support
The survey, for BBC Radio 4's The World This Weekend programme, found that out of the 101 Labour MPs who responded, 22 said they supported the renewal of Trident.
A total of 64 said they opposed it, and a further 15 remained undecided.
Livingston Labour MP Jim Devine, who is parliamentary private secretary to health minister Rosie Winterton, has indicated he will resign over the issue.
The Scottish National Party is urging ministers not to base the replacement in Scotland.
Leader Alex Salmond said Mr Devine's resignation would signal a Labour split.
"The government's Trident replacement policy will loom large over a divided Labour party in Scotland in May," he said.
Mr Salmond cited a government White Paper which states £1bn a year over a period of 15 years will have to be raised from the Treasury budget or from new taxes.
Opposition to the plans could mean the government will have to rely on the votes of the Conservatives to carry Wednesday's motion to determine whether a new generation of nuclear submarines is acquired and the Trident D5 missiles updated.
Mr Browne told BBC One's The Politics Show the UK had an "obligation" to retain a deterrent as part of its membership of Nato.
He said: "It's not nearly as straightforward as people suggest. They sleep soundly in their beds at night because we have nuclear weapons."
Mr Browne added: "Some people feel they are prisoners of the position that the party had before it changed in the 1980s [which was one of unilateral nuclear disarmament]."
He went on: "I'm still confident we will persuade people to come to our side of the argument."
Lord Chancellor Lord Falconer said: "There will be people who take a different view, but I hope we demonstrate that we are broadly unified on the way to go forward."
Shadow defence secretary Liam Fox said the Conservatives were supporting a replacement for Trident to ensure the UK was "prepared for all eventualities".
He added: "When the government is doing the right thing in terms of national security we think they should get the support of the opposition."
Liberal Democrat defence spokesman Nick Harvey said: "I understand that the Tories support Trident's replacement, but surely even they can see that the final decision will not be made until 2012 -14. That's when Parliament should make its decision."
Labour leadership contender Michael Meacher said he would order a new vote on Trident after a "full and proper" public consultation if he won his bid to succeed Tony Blair as prime minister.
The former environment minister said the government was trying to "bounce" MPs into accepting a replacement.