Tory members of the Commons education select committee have drawn up a report pressing the government to go ahead as planned with school reforms in England.
The Education Bill is due before MPs in February
It follows an argument with Labour MPs on the committee over "trust" schools with more say over admissions.
The Tories are calling on the government to have the "courage of its convictions", the BBC has learned.
Earlier, Tony Blair said getting MPs to back the reforms would be a "highwire act", amid backbench Labour opposition.
More than 90 backbenchers have voiced opposition to the plans, seen as central to the prime minister's authority.
The select committee, which has a Labour majority, is due to give its response to the Education White Paper later this week.
The prime minister described the plans as "fundamental" for the government, during his monthly Downing Street press conference on Monday.
Mr Blair says he speaks as a parent first and a politician second
Labour rebels fear trust schools, free of local authority control, would mean children from poorer families losing out because middle-class families would work the system to their advantage.
Tory leader David Cameron has offered to support the government's plans.
The minority report by Conservative members of the education committee opposes any moves to make the admissions code mandatory.
It also says councils should no longer be providers of education.
'Very, very important'
Shadow education secretary David Willetts said Conservatives would "stand shoulder to shoulder" with Mr Blair on his plans because "he is endorsing a principle we have long believed in."
At his monthly media conference on Monday, the prime minister said: "It's a bit of a highwire act... because I've got significant numbers of my own side who are against it."
The issue raised "very, very important" questions for Labour about the role of central and local government, he added.
Mr Blair said he had no intention of losing the legislation, but simply wanted to "level up" standards, adding that the reforms were not a return to academic selection.
"Whenever I look at education, I speak as a parent first and as a politician second," he said.
"I know what I wanted for my own children, what I want for my own children and that is what I expect other parents to want and our job should be to help them to get it, not to stand in the way of them and say we know better than you what's good for your child."
"Is the role of government to help you put power in your hands to do what you want?" he said. "Or is the role of government to tell you what you want?"
Mr Blair said schools would not be forced to become trusts, but would have "permission" to do so.
He said selection by ability was "not a sensible way forward" and it was wrong to divide children up into successes and failures at the age of 11.
"In today's world we can't afford to have anything other than the vast majority of our children getting educated to a very high standard," he said.
The Education Bill, based on the white paper, is due before MPs in February.