As public schools across the country transition to the new Common Core standards, which bring wholesale change to the way math and reading are taught in 45 states and the District, criticism of the approach is emerging from groups as divergent as the tea party and the teachers union.

The standards, written by a group of states and embraced by the Obama administration, set common goals for reading, writing and math skills that students should develop from kindergarten through high school graduation. Although classroom curriculum is left to the states, the standards emphasize critical thinking and problem solving and encourage thinking deeply about fewer topics.

But as the common core shifts from theory to reality, critics are emerging. State lawmakers are concerned about the cost, which the Fordham Institute estimated could run as high as $12 billion nationally. Progressives fret over new exams, saying that the proliferation of standardized tests is damaging public education. Teachers worry that they haven’t had enough training and lack the resources to competently teach to the new standards. And conservatives say the new standards mean a loss of local control over education and amount to a national curriculum. They’ve begun calling it “Obamacore.”

On Tuesday, the head of the American Federation of Teachers and a strong supporter of the Common Core standards will warn that the new approach is being poorly implemented and requires a “mid-course correction” or the effort will fall apart.

“The Common Core is in trouble,” said Randi Weingarten, the union president who is slated to speak Tuesday in New York about the issue. “There is a serious backlash in lots of different ways, on the right and on the left.”

Weingarten is concerned that states are rushing out tests based on the new standards without preparing teachers and designing new curricula.

“This is a wake-up call for everyone else in the country,” she said, pointing to New York, which just administered new tests based on the Common Core standards. Teachers, parents and students complained that the tests were poorly designed, covered material that had not been taught and frustrated children to the point of tears.

New York, like many other states, plans to use the test results in decisions about student grade promotion, teacher job evaluations and school closings. But Weingarten is calling for a moratorium on consequences for at least one year until teachers and students across the country are sufficiently steeped in the Common Core standards. New York and Kentucky are the only states to have begun testing based on the new standards; the others will follow in 2014.

Lucy Calkins, a professor at Teachers’ College at Columbia University , has launched a Web site where hundreds of teachers, principals and parents have posted feedback — overwhelmingly negative — about the new tests in New York.

“I’m a big supporter of the Common Core. I wrote the best-selling book about it,” Calkins said. “But this makes even me question it.”

For President Obama, who encouraged states to adopt the Common Core through policies including his Race to the Top grant competition, the nearly universal embrace of the standards in most states has been a major victory. But as trouble stirs, the administration has kept a low profile to avoid fueling the argument made by conservatives that the Common Core is really a federal intrusion into the classroom.

Two weeks ago, the Republican National Committee called the new standards “a nationwide straitjacket on academic freedom and achievement.”

Lawmakers in GOP-dominated Indiana, which had adopted the Common Core, changed their minds last week and voted to “pause” the implementation so they can have hearings. Indiana Gov. Mike Pence (R) still has to sign off on that new law.

Bills to repeal the Common Core have been filed in Oklahoma, Kansas, Michigan, Missouri, Alabama, South Dakota and Georgia. None of the legislation has passed.

And conservative radio talk show host Glenn Beck has suggested the Common Core represents a move by the federal government to take control of children. “You as a parent are going to be completely pushed out of the loop,” he said on a recent program. “The state is completely pushed out of the loop. They now have control of your children.”

Chad Colby, a spokesman for a consortium of 22 states developing Common Core assessments, dismissed the opposition as a small group of fringe activists.

“If you look at what’s actually going on, when teachers and business leaders stand up in states, they have won the argument,” Colby said. “The far right, this very small, vocal minority, is not winning these battles.”

Curriculum and academic standards traditionally have been determined by states and local communities. That has produced uneven results, with states using a variety of standards. That became clear as students who aced state tests performed poorly on the federally administered test known as the National Assessment of Educational Progress.

Sporadic efforts to create consistent national standards have come and gone.

Several years ago, the National Governors Association began pushing a bipartisan idea of common standards in English and math. The Gates Foundation invested tens of millions of dollars in the effort to write them. And the initiative gained speed when the Obama administration required states to adopt the common standards — or an equivalent — to compete for Race to the Top grant funds or to receive a waiver from the requirements of No Child Left Behind.

By 2012, 45 states and the District had signed onto the math and English standards. Minnesota has adopted only the English standards; Alaska, Nebraska, Texas and Virginia have not adopted either.

The standards are designed to ensure that, for the first time, third-graders in Maine will acquire the same knowledge and skills as their peers in Hawaii. Once states begin testing against the new standards, it will be possible for the first time to compare test scores across communities and states.

For many states, the new standards will be tougher. When Kentucky became the first state to administer tests based on the new standards last year, the percentage of students in middle and elementary school deemed “proficient” or better in math and reading dropped by about one-third.

Education Secretary Arne Duncan declined to take a position on the proposed moratorium but said it speaks to concerns he has heard from educators. “I talk to a lot of teachers,” he said in a statement. “They agree with raising the bar to prepare students for college and career, but some are pretty stressed about the pace and sequence of change.”

Teachers are not opposed to more demanding standards or tests, Weingarten said.

“We have one of two paths,” she said. “We can revolutionize K-12 education to enable kids to be ready for college and career, or these standards can be chopped up with so many well-meaning reforms and end up in the dust bin. . . . We’ve been through this path before about higher standards. Let’s get it right this time.”