John Prescott has told Labour MPs they will not be forgiven if the government has to rely on Tory votes to get through its school reform plans.
Mr Prescott initially had concerns about the plans
The deputy prime minister delivered the rallying call at a meeting of the Parliamentary Labour Party two days before the plans go to a vote of MPs.
Critics fear the plans for England's schools will allow academic selection by the "back door".
A BBC survey of 97 Labour MPs has found that 28 of them would oppose the bill.
These findings suggest the bill will need support from opposition MPs to be passed in the Commons vote.
The Education and Inspections Bill would allow the creation of "trust schools", backed by private firms or faith groups, which would be free from local council control.
Conservative leader David Cameron has pledged his party's support for the plans.
But one MP at Monday evening's meeting of the Parliamentary Labour Party said the "arrogance" of the Tory stance was working in the government's favour.
And Mr Prescott, who has admitted initially being worried about the reform plans, said: "The party and the country would not forgive the Parliamentary Labour Party if the bill was delivered on Tory votes."
Education Secretary Ruth Kelly also addressed the meeting in what one ex-ministers described as a "solid and serious performance".
Earlier Ms Kelly said: "I'm confident that this is a bill we should be able to unite around."
Several backbenchers said it had been a good meeting, with one saying Parliament was in "serious danger of delivering a very good education bill".
But many of the leading rebels did not attend the meeting.
Earlier, the BBC surveyed 97 of Labour's 213 backbench MPs.
Of the MPs who responded, 45 said they would support the government, 28 said they would oppose it and 24 said they had not decided.
Forty-eight Labour backbenchers did not respond to the survey and 68 could not be contacted.
But among the 116 MPs whose intentions are not known, there are 11 members of the Socialist Campaign Group who regularly opposed the government over private sector roles in the provision of public services.
BBC political research editor David Cowling said the figures suggested the government would only be able to secure a second reading for the bill with the votes of opposition MPs.
The Tories say the bill is "timid", but they will back it, while the Lib Dems call the plans a "missed opportunity".
The plans would reduce selection, give headteachers the power to discipline and create new standards for school meals, she added.
Some leading critics of the government's plans last week said they would now support the government when the bill is voted on this week.
Former Education Secretary Baroness Morris, Martin Salter, who resigned as a Commons aide to schools minister Jacqui Smith over the issue, and ex-minister Angela Eagle issued a joint statement explaining their decision to vote for the bill.
The trio were among the authors of alternative proposals which won significant Labour backing.
But they have decided not to block the government's flagship reforms at the first hurdle - although they still have concerns which they intend the tackle as the bill passes through Parliament.