The House is debating changes that would give states and communities more control.

WASHINGTON — The White House threatened Wednesday to veto a Republican bill to overhaul the widely criticized No Child Left Behind law, calling the effort “a significant step backwards.”

The veto threat came as lawmakers began debate on the measure in the House. A vote is expected on Friday.

Republicans say the bill would restore local control in schools and stop top-down education mandates. Democrats say it would allow billions in federal dollars to flow out without ensuring they will improve student learning.

The White House said the bill “abdicates the historic federal role in elementary and secondary education of ensuring the educational progress of all of America’s students, including students from low-income families, students with disabilities, English learners, and students of color.”

The White House statement was the latest in a series of veto threats issued by President Obama since both chambers of Congress went under Republican control last month.

House Speaker John Boehner, R-Ohio, called the education measure “a good conservative bill that empowers America and does not empower the bureaucracy here in Washington.” Boehner called education “the civil right of the 21st century.” A measure pushed by Education Committee Chairman John Kline, R-Minn., would provide states and local communities greater flexibility over how “federal dollars are used to educate America’s kids,” Boehner said.

Kline said education can be the “great equalizer” in America, but only if schools succeed.