Confidence is growing among ministers that the threat of a government defeat over plans to extend detention without charge of terror suspects is receding.
Colleagues of Home Secretary Jacqui Smith believe concessions made by her to rebels have won some of them over.
At a meeting with Labour MPs on Monday, Ms Smith said safeguards would ensure the proposed 42-day limit would be used only in exceptional circumstances.
The Conservatives, Lib Dems and dozens of Labour MPs remain opposed.

'Shifting ground'
Home Office Minister Tony McNulty said he now believed a vote in the Commons next week could be won in the wake of Ms Smith's pledges.
He told BBC Radio 5 Live: "Things do seem to be shifting back to the government's way.
"There's still a lot of work to do, but I'm very hopeful."
Aberdeen North MP Frank Doran had planned to vote against the government, but said he had now changed his mind. He said the "ground is shifting" and although a hard-core of rebels would not be moved, "those in the middle who have had doubts will have heard a lot [from Jacqui Smith] that will have satisfied them".

Ms Smith's concessions are likely to include an earlier Parliamentary vote on any decision to allow a terror suspect to be held for 42 days, a shorter period in which the powers could be used, and a tight definition of the circumstances in which they could be implemented.
Currently terrorist suspects can be held for up to 28 days before they have to be charged or released without charge.
The concessions offered to Labour rebels - previously thought to number about 50 - are expected to be outlined in the form of amendments to the Counter-Terrorism Bill. MPs are to vote on the proposals next week.
Leaving Monday evening's meeting of the Parliamentary Labour Party, Ms Smith said there had been a "constructive discussion" about the promised strengthening of proposals.

'No evidence'
She said MPs should accept her proposals "if they are serious about the security of the country".
But Labour MP John Grogan said while Ms Smith had made a "powerful speech", he was still not convinced she had made the case on security grounds for extending the 28-day limit.
He told the BBC: "We should not give up lightly liberties which have taken centuries to establish. Reluctantly, I still can't support the government."
Another rebel, David Winnick, said: "I haven't changed my views in anyway whatsoever. I don't believe there's any evidence to go beyond 28 days.
"I regret that the measure is going to go, apparently through."
Speaking on Monday, Mr Brown re-emphasised his arguments in favour of extending the time limit.
He said the "scale and complexity" of the terrorist threat facing Britain provided compelling evidence of the need to increase the amount of time suspects could be held without charge.
Security services are pursuing about 2,000 terrorists, 30 potential plots and 200 networks, he said.
Writing in Tuesday's Daily Telegraph, Former Assistant Commissioner of the Metropolitan Police, Peter Clarke, said the 28-day limit would "undoubtedly" soon be insufficient and criticised the politicisation of the debate over the issue.

Mr Clarke wrote that "the terrorist threat is growing in scale and complexity" and rejected claims that an extension would be a threat to civil liberties.
Meanwhile Justice Secretary Jack Straw has accused the Tories of behaving in an "unprincipled" manner over the controversial proposals.
Mr Straw said: "I think they are in a very inconsistent position.
"I'd put any money you like that had they had been in government in the last period, they would have done at least this."
Shadow home secretary David Davis said: "I shall refrain, at this stage, from commenting on the government's reported tactics, both with their own party and other parties. "Its approach now clearly smacks of desperation."