Labour MPs have been holding meetings to discuss the government's newly published plans for schools in England.
Labour rebels fear the reforms may create a two-tier system
Some met the Education Secretary Ruth Kelly who has been trying to win round potential rebels in her party.
The Education and Inspections Bill allows schools in England to set up independent "trusts", with more say over admissions and budgets.
The Tories say the bill is "timid", but they will back it, while the Lib Dems say it is a "missed opportunity".
Concessions, such as banning interviews and a strengthened admissions code, have been included in the bill to win over Labour MPs who fear it will create a "two-tier" system and allow "backdoor" academic selection.
WHAT'S IN THE BILL?
Parents, businesses and voluntary groups to be able to set up foundation (trust) schools, with control over budgets and admissions
Interviewing pupils and parents to be outlawed
Schools to 'act in accordance with' - rather than just 'have regard to' - admissions code
Schools to set up 'partnerships' with outside groups and 'federations' with other schools
Failing schools given one year to turn around or face being closed and replaced
£30m for councils to raise standards
Councils will still be allowed to set up schools, which was something the government's original Education White Paper - published last year - had ruled out.
They will remain as a "strategic commissioner" for education in the area they cover, the bill says.
But Ms Kelly says she is "confident" that her colleagues "should be able to unite around" the bill.
"It is a very good bill. It gives schools the freedoms they need to raise standards," she added.
But BBC political correspondent Carole Walker said many of the wavering Labour MPs who met Ms Kelly on Tuesday evening were not convinced by her reassurances.
Some were more likely to vote against the bill, rather than support it, she said.
Under the plans, failing schools will be given one year to turn around and, if there is no improvement in this time, could be closed, with a replacement school or academy opening on the same site.
Ministers are also promising £30m for local authorities to raise standards in weaker schools.
Private companies, charities, faith groups and parents will be given freedom to set up and run schools under the state system.
Existing schools will be allowed to develop "partnerships" with outside organisations and establish "federations" with neighbouring secondary schools.
The education secretary would retain a veto over councils' attempts to set up comprehensives, but would "not normally intervene".
However, relinquishing the veto is one of the key demands of the rebels.
One Labour backbencher who has reservations about the bill, Louise Ellman, said: "Removing powers from the local authority, who's there to act in the interests of the whole community, is not likely to achieve success for areas who need more support.
"And I think that is the big question mark hanging over this."
Ms Kelly said she would prefer the bill to pass with "the consent of my colleagues", rather than having to rely on Conservative support.
And the prime minister called the reforms a "defining moment" the government.
But Barry Sheerman, chairman of the Commons education committee, said he was now "absolutely sure" Labour MPs would fall behind the proposals when they are voted on next month.
Conservative leader David Cameron said he "would rather (ministers) didn't make concessions".
He added it would be "much better to work with me and the Conservative Party to make sure our children get these reforms".
Liberal Democrat education spokesman Ed Davey told the BBC the bill had not dealt with "selection by the back door".
He added: "There's too much emphasis on structures and not enough on standards."