Education Secretary Arne Duncan said states without waivers will be held to the standards of No Child Left Behind because "it's the law of the land."
Until now, the issue of education has stayed largely out of the presidential race.
But Sen. Mike Enzi, R-Wyo., ranking member of the Senate committee with jurisdiction over education, said Obama was using education as a "political poker chip."
"This action clearly politicizes education policy, which historically has been a bipartisan issue," Enzi said. "It is time for the president to work with Congress on important issues like this instead of acting unilaterally."
And when Rep. John Kline, R-Minn., the chairman of the House Education and the Workforce Committee, released new legislation Thursday that would rewrite No Child Left Behind, it included a provision that prohibits the education secretary from coercing states into adopting specific academic standards in exchange for a waiver.
Duncan maintained this week that the administration "desperately" wants Congress to fix the law.
In an election year in a divided Congress, action on Capitol Hill appears unlikely.
Associated Press writers Dorie Turner in Atlanta, Kristen Wyatt in Denver, and Ken Miller in Oklahoma City contributed to this report.
Education Department flexibility: http://www.ed.gov/esea/flexibility