More than 25,000 people have signed a petition calling for the end of Sats, it was announced today, as industrial action over the tests moved a step closer.
The petition urges the Government to abolish national curriculum tests, known as Sats, for seven and 11-year-olds in England.
Tens of thousands of teachers and head teachers will begin receiving ballot papers asking for their opinion on the tests this week.
The National Union of Teachers (NUT) and the National Association of Head Teachers (NAHT) are holding an indicative ballots and surveys of members over proposals to boycott next year's tests.
The two unions passed resolutions at their annual conferences earlier this year proposing to take joint action to boycott if the tests are not scrapped.
Between them, the two unions represent a large proportion of teaching staff in primary schools.
At a conference in central London today, NUT general secretary Christine Blower made it clear that the union was not proposing strike action.
Instead, if a full ballot is passed, members would refuse to play any role in administering or delivering the tests.
"If both ourselves and the NAHT were determined, and we hadn't got sufficient change, it would be impossible for the tests to be administered," she said.
"Between us we have the vast majority of teachers and school leaders in our membership."
Under the indicative ballot, NUT members will be asked if they would show support for a boycott if a solution is not found. A full ballot would still be taken at a later date, expected to be next Spring.
The NAHT are conducting a survey of their members, which would also be followed by a full ballot later on.
The two unions want to see Sats replaced by teacher assessment.
They argue the tests are bad for children, teachers and education, and cause unnecessary stress.
NAHT general secretary Mick Brookes today said that the tests narrow the curriculum for pupils, and rejected suggestions by the Schools Secretary Ed Balls that teachers should not rehearse children for the tests.
"That is like telling an Olympic high jumper not to practice before the Olympics."
Mr Brookes added that any boycott next May is likely to coincide with a general election.
"Who are we going to be up against with this? Michael Gove (the shadow school secretary) has already suggested he doesn't want Sats in Year 6, it would be difficult for him to complain if we don't do them."