The forthcoming review of primary Sats testing needs to radically change the system or unions could boycott the 2012 exams, they claimed this week.
Russell Hobby, general secretary of heads' union the NAHT, said that if the Bew review - due in June - did not result in substantial "movement" in the system they would considered a ballot on a boycott.
At a launch of a joint union position statement on primary testing, Mr Hobby said: "If there's no movement in the system that puts us exactly where we were this year (in September 2010). Our members expect 2011 to be the last year of the regime."
But he added that he "had faith" in the review process and believed it had the potential to produce the changes unions are demanding.
The panel selected to carry out the review includes a number of primary heads, something the NAHT insisted on before accepting it in return for calling off a boycott in 2011.
The review will report just as the pilot of a national reading test for six-year-olds is launched.
Mary Bousted, general secretary of education union ATL, which did not boycott Sats last year, said her union "would have to reconsider its position" if the review did not result in change. "Anything other than a radical revision will be greeted with contempt," she added.
Ms Bousted said that even the former Labour schools minister Jim Knight had admitted the current testing regime had been pushed as far as it could go. "This government has a huge incentive to make the required changes to ratchet up educational standards again."
Kevin Courtney, deputy general secretary of the NUT, also refused to rule out considering a boycott should the review, or the Government's reaction to the review, be disappointing.
The three leaders spoke out as they launched their document Common Ground on Assessment and Accountability in Primary Schools, which calls for an end to league tables, and for a system of externally moderated teacher assessment coupled with national sampling to be introduced.