Education Secretary Ruth Kelly urged Labour MPs to back controversial schools reforms in a crucial vote this week - pledging more discussions of key concerns.
She refused to predict whether Tony Blair would have to rely on Conservative votes to get his flagship plans for independent state schools through the Commons on Wednesday.
But she said it was legislation "we should be able to unite around", repeating her insistence that it would help, not hinder, pupils from poorer backgrounds. And she suggested some of the opposition to the proposals for "trust schools" backed by private firms had been sparked by false reports from the Opposition.
Some leading members of the backbench rebellion against the plans indicated this week that they would vote with the Government in the Second Reading vote.
Martin Salter - who quit as a Commons aide to schools minister Jacqui Smith over the issue - and ex-minister Angela Eagle said they would instead seek to change the Bill at a later stage. Asked if she thought enough colleagues would join them to realise the Prime Minister's call for it to be a "Labour" Bill, she said: "I'm not going to get in to the numbers game.
"But what I can say to you is that we have a set of proposals which I think every Labour MP should be supporting because it's a set of proposals that has the potential to raise standards for all schools, but particularly for schools that operate in disadvantaged areas, with a high proportion of children on free school meals, and that's where we really need to make the difference."
Asked whether she felt her job would be on the line if the legislation was approved only because of Tory support, she
said: "I'm confident that this is a Bill we should be able to unite around.
"And yes, it's my job to go to talk to people, to take them through the provisions in the Bill . . . we have a Bill which is a Labour Bill, which will deliver not just for all children but particularly the disadvantaged, which puts looked-after children first, where there's less selection after the Bill than before . . . which gives head teachers the power to discipline, first proposed in 1988 and rejected by the Tories, which introduces an entitlement for vocational education, for the first time in this country's history, which introduces new standards for school meals and puts healthy food on every child's plate.
"An incredibly strong set of proposals which every Labour MP should support."
A number of concessions have already been made in a bid to quell the significant Labour backlash against the plans.
Asked if she expected to make more, Ms Kelly said: "The movement that we've made to date is part of the ordinary passage of a Bill between White Paper stage and Bill stage, and it will be the Committee stage, in which we continue that dialogue with colleagues.
She said she would aim to "pin down as firmly as possible" how a veto for the Secretary of State over the right of local councils to open new schools would operate.
That is one of the key concerns of rebels still to be addressed.
Former education secretary Baroness Morris joined Mr Salter and Ms Eagle in issuing a statement last week explaining their decision to vote for the Bill.
All three were co-authors of an alternative proposal which had won significant backing in the party.
While the measures were still "far from perfect", they should not be blocked at their first hurdle, they said.
Mr Blair said last week that he would "prefer" to get the reforms through Parliament with the support of all his backbenchers.
"It is a Labour measure because it is about raising standards on the basis of equity and fairness but making sure we don't tolerate fail-ure," he said at Downing Street.
The reforms propose a new generation of independent "trust schools" - state schools free from local authority control and backed by businesses, faith groups or other organisations.
Ministers argued that the reforms would help good schools collaborate with weaker schools to raise standards. But critics - at one time including deputy Prime Minister John Prescott - raised fears children from poorer families would lose out.