The last attempt was in 2012, the second session of the O’Brien legislature.  It failed in a big way.  You can dig into all the detail here.  But post mortem by Kevin Landrigan, then with the Nashua Telegraph, “Legislature’s power figures took it on the chin with education funding vote”, is the best political overview.  The over-all themes are still very relevant:

Don’t let anyone kid you.

All those in power in Concord lost something when the education funding amendment went down to crushing defeat on Wednesday.

To be sure, the defeat was the most acute and potentially damaging to William O’Brien, R-Mont Vernon, who staked much of the success of his first term as speaker on getting an amendment to the voters.

When the House of Representatives passed an amendment for the first time ever in March 2011, it was looking like the dam was finally broken that with this awesome 3-1 majority rule, the Republican-led Legislature was going to get it done.

Sixteen months ago, only 20 Republicans defied O’Brien’s wishes and opposed the amendment.

Last week, the dissident number more than doubled.

But this was also a top priority for Senate President Peter Bragdon, R-Milford, and one Gov. John Lynch highlighted in each of his last two state-of-the-state speeches.

They can all “celebrate’’ having gone further than any other campaign since the landmark Supreme Court ruling 15 years ago.

That’s cold comfort.

With only 10 percent of Democrats in the House backing this amendment, it could have passed.

But given Lynch’s status as a lame-duck governor and long-standing opposition in the Democratic base to any such proposal, that wasn’t going to happen, even if the governor had done real work to try to change it.

And there’s little concrete evidence Lynch did.

So what was the profile of those House Republicans who voted no when it really counted?

…..This was the death of one or two cuts here or there spread across the state – 16 no votes from Hillsborough County, 18 from Rockingham County.

Clearly, the Republican Liberty Caucus of New Hampshire had more influence this time than it did when O’Brien handily won Round 1.

Why? The wording, of course, and it isn’t like O’Brien was caught by surprise.

More than a month ago, former Gov. John H. Sununu, gubernatorial candidate Ovide Lamontagne, and constitutional lawyers Eugene Van Loan and Chuck Douglas met privately with a key group of the libertarian “constitutionalists,” for lack of a better way to describe them.

The pitch was: Could they support an amendment that had the state assuming the “responsibility’’ for maintaining a public education system?

The answer was nearly unanimous, according to sources who were there.

No way.

…..Every chief executive since Claremont I has proposed or endorsed an education funding amendment. That’s five governors – three Republicans and two Democrats – and several governors who served before them have gotten onboard.

To any chief executive, this has always been about the balance of power.

Making aid to public education a fundamental right with a per-pupil grant requirement has been an anathema to them.