I should have described what I think the main differences are between NHELD and HSLDA's approaches. NHELD is more of an 'originalist' when it comes to rights. We are guarenteed rights in the constitution and it is better to have those rights recognized than to further the myth that the only rights allowed to citizens are those actually enumerated in the constitution. If the only rights are those that are enumerated, then we can expect our constitution to become quite unwieldy as each right needs to be added.
I think the idea is that if HSLDA gets some kind of federal law pertaining to home school, there will be more incentive to get their constitutional ammendment passed. One of the main reasons for not supporting it is that it would make home school law-making a federal responsibility. If you can say that homeschooling is already a federal responsibitity, the switch goes from fighting it to trying to modify it. NHELD has spoken against this--it's harder to fight at the federal level (and others more legally based than pragmatic).
As you can guess, NHELD and HSLDA are at odds about how homeschooling rights should be defended. I am completely on board with NHELD and regard HSDLA suspiciously, given their other agendas. Moving homeschooling to a federal venue would negate NHELD's abilities to be a voice for homeschoolers. One main attorney, no matter how great her heart, will not have the resources that HSLDA has, given their broad donation-base of Christians who are hoping to mandate their morals in federal law.
NHELD works on a basis of ideology. There is no double-talk. When NHELD comes out against something, you know what they believe and what their grand plan is. They don't just want bits and pieces of seemingly OK legislation. They want to try to pass the best, most rights-protecting, wording. I love NHELD.
HSLDA is much more of an expediency advocacy group (which I am against just as much as I am against their theoacratic leanings). Whatever seems to work at the time to get a little closer to their final agenda is OK with them.