Those rebelling against the leadership line will urge the union's annual conference to back an immediate boycott of tests at 7, 11 and 14 and launch a "nationwide campaign of opposition to tests and league tables".
Testing and targets are among the hottest issues at this year's teacher union conferences.
The National Association of Schoolmasters Union of Women Teachers will publish research on the damage caused by the over-testing of pupils and by league-tables at their conference next week.
But Eamonn O'Kane, NASUWT general secretary, said that the union's national executive would not support any calls to join a boycott of tests because the action would be illegal.
"There may be a strong philosophical argument for it but that would not cut any ice in the courts," he said.
Last month, the NUT's executive voted narrowly to reject calls to ballot members over tests at 7 and 11 because senior figures did not want the union to be isolated on the issue.
Instead the union has issued guidance to members advising them to refuse to take on extra bureaucracy for tests that is not required by law.
John Bangs, NUT head of education, refused to predict the outcome of any vote but admitted that there is "a real head of steam building up" among teachers for change.
Shadow Education Secretary Damian Green is expected to lend his voice to growing calls for the Government to scrap many of targets for schools when he addresses the NUT on Monday. He will try to win teachers' support by expressing concern that targets are damaging children's education. Some primary schools spend up to a year coaching pupils for key stage 2 tests, leaving them ill-prepared for secondary school, he will say.
But Mr Green will not support a test boycott, saying that it is the Government's targets that do the damage.
In February chief inspector David Bell said that targets were becoming counter-productive.
Leaders of the NUT, NASUWT and Association of Teachers and lecturers will meet after the conference season in an attempt to agree a common campaign against national tests.