As the union prepares for its spring conference in Torquay next week, there are clear signs that the leadership's boycott strategy will fizzle out.
According to a survey by The TES, governors are unwilling to breach their statutory obligation to complete the test results. Many expressed surprise that the NAHT should ask them to act illegally, while advising its own members not to. Others felt that refusing to return teachers' assessments of pupils - the only part of the tests which the Government could not obtain from examiners - would be counter-productive.
Phil Smith, chair of the Leicestershire Association of Governors, expressed a typical view: "We are vigorously opposed to the Secretary of State's decision, but we are not prepared to refuse to send in the results. The Government will be able to get the test results from the markers. The only part it would not get is the teachers' assessment, which is the bit that really matters."
Roger Adcock, a primary school governor in Devon, added: "I don't think the moral standing of our governors would benefit by trying to break the law. At the same time, we would certainly want to protest."
In Nottinghamshire, where the county council is developing its own "value-added" assessment system, some primary schools have refused to take part in the KS2 tests (see story below).
Other governors are angry but reluctant to break the law, according to Gill Lane, chair of the county's association of governors. Having sought independent legal advice, the association believed refusing to return test results would be a civil offence rather than a criminal offence. But if resistance continued, governors could be personally liable.
"Governors are sympathetic to the NAHT's cause, but the fact that in order to support it they would have to breach their statutory obligations makes them very nervous," Ms Lane said. "I get the impression that if the legal position was clearer, governors would support action more strongly."
Arthur Phillips, a member of the National Governors' Council in Haringey, north London, was unwilling to boycott teacher assessments. "If the headteachers want to fight, good luck to them but they should do it on their own."
Ruth Tindley, general secretary of the Association of Northamptonshire School Governing Bodies, said members wanted the introduction of league tables to be delayed for a year.
She added: "We don't want conflict with headteachers - basically we are on the same side - but I am a little disturbed that they have asked governors to break the law."
Susan Marsh, treasurer of the NGC national executive and chair of the governing body at St Mary's C of E primary school in Droylsden, Tameside, said: "Governors do not want to break the law. I dislike being put into the position of having to make that decision by Gillian Shephard telling us she wouldn't publish the test results and then changing her mind."
Sandra Tomlinson, chair of the Sheffield Association of Governing Bodies, said governors would be "shooting themselves in the foot" if they withheld their teacher assessments. "It's not that we are afraid of breaking the law, but we don't think it is worth it on this occasion."
Helen Vaile, a governor of Y Bont Faen primary school in Cowbridge, Glamorgan, ruled out breaking the law. Expressing her personal view, she said: "I'm quite happy for the results to be published because that is the way to raise standards."
But John Mitchell, secretary of the Wirral governors' association, said: "I would support refusing to co-operate with the test results. I am chair of the governing body at a school in a very deprived area and I would be very unhappy for its results to be published in a league table."
Sue Birkin, chair of governors at a primary school in Rotherham, said: "My personal view is that if the headteachers are not prepared to break the law they should not be asking us to do it.
"But I am totally against publishing the results. I have a son who has done the KS2 tests and the pressure on him and on the school has been enormous."