More than 10,000 people have signed a petition calling on the Government to scrap controversial key stage 2 tests.
The petition was launched by the NUT and the National Association of Head Teachers as part of their high-profile campaign to get rid of the exams.
The two unions have said they will ballot their members to boycott next year's Sats unless the Government pledges to radically alter the tests and replace them with teacher assessment.
This term will be crunch time for the unions in deciding if they have the backing of their members in carrying out the boycott. The NUT will hold an indicative ballot of its members and the NAHT will hold a formal consultation run by an external company to gauge the level of support from their members.
"There was an accusation that the boycott was out of touch with our membership," said Mick Brookes, general secretary of the NAHT. "We don't think that is true, but want to be sure of our position.
"We are determined that this year top primary pupils will receive a broad and balanced curriculum, unhindered by the mind-numbing rehearsal of past Sats papers."
Mr Brookes said the union continued to be in negotiations with the Government and hoped agreement could be reached that would make the boycott unnecessary.
Christine Blower, general secretary of the NUT, said the petition had been signed by concerned parents as well as teachers. It has also won the support of Michael Rosen, the former children's laureate, and author Philip Pullman.
"Getting so many people signing our petition is a clear indication that we are not alone in our concern about the detrimental effects that Sats have on our education system," said Ms Blower.
"They are bad for education, bad for children and bad for teachers. They encourage teaching to the test, a narrowing of the curriculum and the unfair and misleading system of league tables."
Michael Rosen has described the tests as "utterly useless". "They drive children, teachers and parents nuts," he said.
The NAHT admitted ahead of its conference in May this year that there was a "lot of nervousness" among heads about the boycott and work was needed to win them over.
Polls carried out around the same time suggested that action would not win the widespread backing of parents. Fewer than half of parents agreed it was appropriate for teachers and heads to carry out the boycott, according to a survey by the National Confederation of Parent Teacher Associations conducted in May.
The findings followed contradictory findings from independent survey commissioned by Government. Seven out of 10 parents said tests provided valuable information, but fewer than half thought they should remain in their current form.
The NUT will launch a separate petition at the Liberal Democrat conference in Bournemouth this weekend against the proposed licence to teach, which the Government wants to introduce. Under the plan teachers will face a check every five years that they are fit to teach.
Ms Blower said she could understand the need for checks if teachers had been out of the classroom for a number of years, but not otherwise.
"There are already any number of systems by which teachers are measured and assessed," she said. "A licence to teach for everybody is overkill."