In the struggle to fix the nation’s public schools, the old red-state, blue-state idea is looking as dated as Dick and Jane. You can hear the change in the voice of Gov. Butch Otter, a Republican in one of the most deeply conservative corners of the country, when he expresses a brotherhood bond with Rahm Emanuel, the Democratic mayor of Chicago and former Obama administration chief of staff.

“I could empathize with Rahm and what he was going through,” Otter said about the recently settled teacher strike in Chicago.

“It’s not the teachers,” Otter said, paraphrasing Emanuel’s tough-guy script from a news conference at the height of the standoff. “It’s the union bosses.”

Chicago’s fight may be over, but in Idaho, where a three-part proposition on performance pay, tenure and technology in the classroom is roaring toward Election Day, the debate over schools has morphed into a harsh discussion about whom the voters should trust.

And as Otter’s attack line shows, the political and social battle lines are blurred — neither predictably conservative nor liberal, and often tinged with emotion about what schools can and might be.

South Dakota and Michigan also have questions on their ballots that ask voters to weigh in on collective bargaining issues. Voters in California and Arizona will decide on new or expanded taxes to support their schools. At least 20 state legislatures addressed teacher tenure this year, most of them shifting power from unions to districts, according to the National Conference of State Legislatures, a nonpartisan group.

But Idaho’s track through the faculty lounge — closely watched by labor and education interests around the nation — is still a case apart in the magnitude of the changes and how they came to be.

In a mostly rural state where the recession was particularly brutal in construction and manufacturing, lawmakers carved some of the deepest cuts in school spending in the nation. Per-pupil outlays fell 19 percent between fiscal 2008 and 2013 — only Arizona, Alabama and Oklahoma cut more — according to a report by the Center on Budget and Policy Priorities, a policy research group focused on low- and moderate-income families.

In 2011 the Legislature passed, and Otter signed, a regulatory overhaul of public education: eliminating tenure and stripping teachers of most collective bargaining rights, yet promising hand-held computers for students.

That created the context that both sides are now fighting over in television ads and political broadsides. The teachers’ union and its allies wonder if the state’s regulatory changes were sincerely aimed at improving schools, or a cynical move — with the recession as cover story — to eliminate one of the last vestiges of union life in a fiercely anti-union state.

The governor and his allies ask if teachers really want the best for students, or if they are fighting to defend cushy rights in setting schedules and curriculums that few other workers enjoy.

FROM OHIO TO IDAHO

Whether public employees in general have it too good in a transformed global economy is a question in a number of states. Last year, Ohio residents struck down a package of laws that reduced public employee perks. The recall election in Wisconsin this year was a public-worker debate by proxy, as Gov. Scott Walker, a Republican who had pushed through a rights-reduction package, was reconfirmed.

In Idaho it is all about what happens in the classroom.

AUSTERITY, CREDIBILITY

“If you look at polling, union leaders are one of the least respected when it comes to getting information about education, but teachers are always at the top,” said Tom Luna, Idaho’s superintendent of public instruction, who led the overhaul drive.

Firing back, teachers and their union representatives say the overhaul, formulated during Idaho’s application for federal funds in the Obama administration’s Race to the Top education incentive program, was mostly about austerity.

Luna “tried to claim there was a need for reform, when in actuality it was a political answer to our economic conditions,” said Robin Nettinga, the executive director of the Idaho Education Association. The association, representing about 13,000 teachers, led a petition drive this year to challenge the overhaul package and put it on the ballot. Its yard signs urge voters to strike down “the Luna Laws.”

Some district administrators say they fear that in their bloodletting both sides are forgetting the students.