Proposals to boycott Sats in primary schools have failed to win the unanimous backing of teachers' leaders, despite the deep unpopularity of the tests.
The National Association of Head Teachers and the NUT have said they will hold votes at their annual conferences on whether to boycott tests for seven and 11-year-olds in 2010.
The continuation of tests beyond this year would be "unacceptable for the future of children's education", the unions have warned.
Mick Brookes, general secretary of the NAHT, said his members were still "livid" that they were having to administer national key stage tests after they were scrapped for 14-year-olds in October last year.
Christine Blower, acting general secretary of the NUT, said that primary schools' patience had been "stretched to the limit and beyond".
"Our deadline for the end of Sats of 2010 is reasonable, and our alternative is one which will enhance teaching and learning," she said.
"Above all else, the Government needs to understand that this year's national curriculum tests will be the last."
The two unions are calling for teacher assessment to be the main way that pupils are judged at KS1-3. They also want the introduction of a national sampling scheme, which would test a small number of pupils, to gauge standards in English, maths and science.
The possible introduction of "when ready" tests, currently being trialled, would not put a halt to the boycott, they said.
But Mary Bousted, general secretary of the Association of Teachers and Lecturers, said that while she agreed with those principles, a boycott was the wrong way to achieve them. "The idea that a boycott will sway the Government is naive," she said. "If anything, it is likely to make them more intransigent."
Chris Keates, general secretary of the NASUWT, said the entire school accountability regime needed to be radically overhauled.
"Simply removing the tests will do teachers no favours at all," she said. "The important thing is to get rid of league tables."
The Voice union said the Government's "obsession with testing" had distorted the curriculum, but also said it would not back a boycott because conducting the tests was part of teachers' duties.
Heads have a statutory responsibility to administer key stage tests. But Mr Brookes said the NAHT was confident that, having taken legal advice, members would not face problems if the boycott went ahead.
A government spokesman said a boycott would remove basic rights from parents to see how their children and schools were performing.
"Action to disrupt the smooth running of national tests would be a disappointing and irresponsible step," he said.
National tests for 14-year-olds were scrapped last year after problems led to severe delays in returning test marks. The Schools Secretary, Ed Balls, set up an "experts' group" to advise on the future of testing and assessment, which is due to report in the spring.