WASHINGTON — The health care law may be Republicans’ favorite weapon against Democrats this year, but there is another issue roiling their party and shaping the establishment-versus-grass-roots divide ahead of the 2016 presidential primaries: the Common Core.

A once little-known set of national educational standards introduced in 44 states and the District of Columbia with the overwhelming support of Republican governors, the Common Core has incited intense resistance on the right and prompted some in the party to reverse field and join colleagues who believe it will lead to a federal takeover of schools.

Conservatives denounce it as “Obamacore,” in what has become a surefire applause line for potential presidential hopefuls. Other Republicans are facing opprobrium from their own party for not doing more to stop it. At a recent Republican women’s club luncheon in North Carolina, a member went from table to table distributing literature that called the program part of “the silent erosion of our civil liberties.”

The learning benchmarks, intended to raise students’ proficiency in math and English, were adopted as part of a 2010 effort by the National Governors Association and the Council of Chief State School Officers to bolster the country’s competitiveness. Some conservatives, in an echo of their criticism of the health care law, say the standards are an overreach by the federal government.