When the final Common Core State Standards were released in 2010, they were notable, in part, for how little opposition they generated.

After prior attempts to create uniform national standards had failed, that goal seemed to have finally been accomplished, and in a way that was bipartisan. Kentucky was the first state to sign on, and two months after the standards were released, more than two-thirds of states had adopted the standards. With few exceptions, educators hailed them as a big improvement for most states, a chance to give some uniformity to education expectations across the United States and ensure that students graduate from high school with a deeper understanding of subjects, better critical thinking skills, and thorough preparation for college courses.

Fast-forward four years, and the headlines about Common Core are mostly consumed with who is dropping out – either from the standards themselves or from one of the two tests designed to assess them – or who is being pressured to do so.

The backlash is coming from both sides of the political spectrum. Among Republicans, supporting Common Core (aka “Obamacore”) has become particularly toxic, with numerous politicians up for election this fall or maybe in 2016 vehemently reversing prior support. Criticism is almost as strong among some segments of the left, albeit for different reasons. And for both sides, Common Core seems largely to have become a proxy for whatever in education people are unhappy with.

For most states, this school year will be the first that the standards will be both fully implemented and tested, and it’s an open question what will be the degree to which the backlash affects that process or the standards’ effectiveness.

“The politics have reached the point where they’re getting in the way of actually implementing” the standards, says Andrew Rotherham, cofounder of Bellwether Education Partners, an education research and policy group based in Sudbury, Mass.

“The perception is one of momentum [for the anti-Common Core people], and politics is a game of perception,” he says. “If you end up with 25 states doing [Common Core] in a meaningful way, that’s an enormous victory, but it won’t be perceived that way.”

Most people agree that for Republicans, the seeds of the backlash were planted when President Obama and Education Secretary Arne Duncan got behind the standards, encouraging states that wanted to apply for federal Race to the Top funds to either adopt the standards or adopt comparable ones deemed “college- and career-ready.” [Editor's note: The original version of this paragraph overstated the expectations placed upon states applying for Race to the Top funds.]

What had been sold as a state-led effort, supported by the National Governors Association, suddenly became associated with Mr. Obama, and rumors circulated quickly of a national curriculum (the standards don’t actually prescribe curriculum) and a federal takeover of education.

“If it weren’t for the Race to the Top funds and the No Child Left Behind waivers, you wouldn’t have had 45 states sign on,” says Shane Vander Hart, a conservative anti-Common Core activist. “There was executive overreach.”

To date, the states that have actually dropped the standards – Indiana, Oklahoma, and South Carolina – are red states. Also, Missouri and North Carolina have made moves toward dropping the standards. Louisiana Republican Gov. Bobby Jindal, who used to be a strong Common Core supporter, has done an about-face and has tried (unsuccessfully so far) to withdraw his state from both the standards and the new tests. Governor Jindal is considered to be a presidential contender for 2016.

But there has also been vocal opposition from blue states – some around the standards themselves, particularly for younger grades, but much of it around implementation, as well as the tests and high-stakes consequences tied to the new standards. The varied quality of “Common Core-aligned” textbooks hasn’t helped. This spring, the Chicago Teachers Union became one of the biggest local unions to officially oppose Common Core.

Bianca Tanis, an elementary special-ed teacher in Rockland County, N.Y., says many of the standards are “grossly inappropriate,” especially for young students.

Common Core, for instance, places a strong emphasis on “text-based evidence,” even in elementary school. Ms. Tanis says that while that may be fine for older students, asking third-graders to constantly go back to the text to explain answers is not only inappropriate, but also tedious.

“You have children who are reading, then furiously going back and looking for text-based evidence,” Tanis says. “It has them stuck on two pages of ‘Peter Pan’ for weeks. It’s taking the joy out of it, preparing them to be workers and preparing them for a test. Is that what education is?”

Still, a solid majority of teachers – about three-quarters, according to most polls – support Common Core. The two largest teachers unions – the National Education Association and the American Federation of Teachers – have been supporters, although they’ve been critical of the standards’ implementation and the high-stakes consequences attached to the new tests.

In June, even the Bill & Melinda Gates Foundation – a major catalyst in the development and adoption of Common Core – called for a two-year moratorium on high-stakes decisions for teachers or students based on Common Core assessments.

“If you suspend accountability for two to three years, a lot of the political problems around Common Core, the mounting opposition, certainly from the left, goes away,” says Patrick McGuinn, a political science and education professor at Drew University in Madison, N.J.

But some wonder if unions might turn a temporary delay into a more permanent one.

Some of the standards’ biggest advocates are educators who say they’ve seen the difference the standards can make. A basic Common Core idea is that the standards are supposed to emphasize depth over breadth, ensure students really master concepts, and build on previous learning (“scaffolding” is the term some educators prefer).

Britton Kilpatrick, a high school math teacher in Ruston, La., says the difference he’s seen is huge.

“Before, the Louisiana standards were entirely focused on ‘Can you do the procedure? Do you know the algorithm?’ ” says Mr. Kilpatrick. Common Core, he says, “wants them to understand math deeply, so by the time they get to middle and high school, they’ll be able to do this math and move at a different pace, because they will understand the foundational stuff.”

The first few years with the new standards have been challenging, Kilpatrick acknowledges, mostly for students who came into advanced math courses without having the understanding they needed to meet the Common Core standards. But he says he’s already seen huge growth for some students, and he expects it to get better with each year.

But he’s concerned about the politics – that Louisiana could even withdraw from Common Core or the new assessment in the next few months. “I’m worried that all the political ideas about big data or a federal takeover are getting so intermingled with the actual Common Core standards that I’m afraid they’ll poison the good that can come from the standards,” he says.

In New York, one of the blue states where opposition has been most heated, Melissa McLean says she was initially apprehensive about Common Core when she knew her son Elijah, who just finished third grade, was going to take a new test aligned to the standards. But Ms. McLean went to meetings at her son’s school, Achievement First Endeavor in Brooklyn, visited his classroom, and slowly got comfortable with the new material.

“The kids don’t just need to have the regular ‘I can memorize 1 + 1’; they need to have the critical thinking skills. That’s what I want for my son,” McLean says. “They’re teaching him how to multiply and divide, and [students] can answer the question ... three different ways. I had a book with the multiplication table in the back, and I had to memorize it.”

Stephanie Keenoy, the principal at Endeavor, says she’s worked hard to help both teachers and parents at the school understand and support the shift. Common Core has meant a big change not just in what the students are learning and how they’re learning it, she says, but also in what teachers’ and parents’ image of success is.

“It’s no longer about students getting 100 percent [on tests]; that’s not what makes an excellent teacher,” she says. “It’s about setting an unbelievably high bar, and when kids don’t hit that bar, we help them get there.”

Despite the backlash, Common Core is entrenched in a majority of states. Even Mr. Vander Hart, while he’s pleased with some recent successes for the opposition, acknowledges that his movement is “an uphill climb.” “You have [most] states still Common Core-aligned, and you have Gates’s money behind it. It’s definitely a David versus Goliath situation,” he says.

Some states may keep the standards but drop out of the new assessments or implement Common Core in name only.

“Standards are just words on paper,” says Frederick Hess, director of education policy studies at the American Enterprise Institute, a conservative think tank in Washington. In the end, he says, there may be just 15 states that are really serious about implementing and testing the standards, but Common Core will be judged based on the results in all the states that technically have adopted them.

Judging Common Core’s success could take some time, notes Michael Brickman, national policy director at the Washington-based Thomas B. Fordham Institute, which has largely supported the standards. “Supporters or opponents who are looking for dramatic doomsday or utopian results from Common Core are going to have to wait. High standards is but one piece in the education reform movement,” he says.