Susan Walsh, Associated Press
In this Jan. 21, 2015 file photo, Senate Health, Education, Labor and Pensions Committee Chairman Sen. Lamar Alexander, R-Tenn. listens to testimony on Capitol Hill in Washington

WASHINGTON — The Senate has cleared the way for a vote by Thursday on a bipartisan bill to rewrite the George W. Bush-era No Child Left Behind education law.

Lawmakers have been considering the bill since last week. They voted Wednesday to limit additional debate on further changes to the legislation and move forward to a vote on final passage.

The bill, sponsored by Sens. Lamar Alexander, R-Tenn., and Patty Murray, D-Wash., would narrow the federal role in public schools by giving states and school districts more control over assessing the performance of schools, teachers and students.

It would keep No Child Left Behind's requirement for annual math and reading tests but prohibit the federal government from requiring or encouraging specific sets of academic standards, such as Common Core.

Common Core was drafted by the states with the support of the Obama administration, but the standards become a rallying point for those who want a smaller federal role in education

Senators intended to spend the next day discussing dozens of amendments before a final vote. Any bill that emerges from the Senate would then have to be reconciled with a more conservative version that the House passed last week.

The House bill, sponsored by Rep. John Kline, R-Minn., also lessens the federal role in education policy by turning more power over to the states to assess school performance and by preventing the administration from pushing Common Core on the states.

This bill also allows federal money to follow low-income children to public schools of their choice, an issue known as portability. Democrats do not support it.

Education Secretary Arne Duncan has said the White House would veto the House measure. Duncan has been more supportive of the Senate bill, but has urged changes that would require states to identify their lowest-performing schools and require those schools to have plans for improvement.

No Child Left Behind, which had bipartisan support and was signed into law by Bush in 2002, mandated annual testing in reading and math for students in grades three through eight and again in high school. Schools had to show student growth or face consequences. But critics complained there was too much testing and the law was too punitive on schools deemed failing.

The law has been up for reauthorization since 2007.