Labour MPs should vote for the education reforms or risk division, chairman Ian McCartney has warned.
Ian McCartney said MPs should not defeat their own government
He said the Labour by-election loss last week showed that party disunity would not be tolerated by voters.
Mr McCartney said Labour MPs had "a strong sense of purpose" and were elected on a joint manifesto.
"Our manifesto can't be a pick and mix," he warned, adding that MPs should not "collaborate with the opposition parties' whips to defeat Labour".
The Education White Paper proposes setting up independent "trust" schools, with more say over admissions.
More than 90 Labour backbenchers, fearful that this could lead to academic selection "by the back door", have signed up to an alternative version, prompting fears that the government may have to rely on the support of the Conservatives to push through the legislation.
Mr McCartney, speaking at the party's spring conference, praised Labour MPs who wanted to improve the proposals before they became a bill later this month.
However, he said that Labour supporters knew the difference between them and "a handful of Labour MPs who would go so far as to collaborate with the opposition parties' whips to defeat their own Labour government.
"That is not a line Labour MPs should cross," he warned.
Other senior party officials have said the by-election defeat in Dunfermline was due to local issues, giving the Liberal Democrats a seat previously held by an almost 12,000 Labour majority.
But Mr McCartney said: "The backdrop of the last few days offers a powerful lesson to us all.
"If some Labour MPs are determined not to vote Labour in Parliament, how can we expect our supporters to be determined enough to vote Labour at the ballot box?"
He urged rebels to back independent state schools, which he said would tackle the "culture of low expectation" that saw him leave the classroom to become a joiner.
"We want to create a culture of high expectation because it's that thing called aspiration, where our people become the best they can be," he said.
"All our previous major reforms in education have been delivered in the face of opposition and they have all delivered for millions of children."