Senators have been considering the bill since last week. They voted 86-12 to limit additional debate on further changes to the bill and move forward to a vote on final passage on Thursday.
The bill, sponsored by Sens. Lamar Alexander, R-Tenn., and Patty Murray, D-Wash., would narrow No Child Left Behind's federal involvement in public schools by giving states and school districts more control over assessing the performance of schools, teachers and students.
It would keep the law'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. Drafted by the states with the support of the Obama administration, the Common Core standards have become a rallying point for those who want a smaller federal role in education.
Any bill that emerges from the Senate would have to be reconciled with a more conservative bill that passed the House last week, with few votes to spare. No Democrats supported it, and 27 Republicans voted against it.
Like the Alexander-Murray bill, the House legislation sponsored by Republican Rep. John Kline of Minnesota reduces the federal role in education policy by turning more power over to the states to assess school performance and by preventing the Department of Education from pushing Common Core or other standards on schools.
The Kline 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, and portability was voted down in the Senate last week.
Senators held four floor votes on amendments to the bill on Wednesday. All of them failed.
The White House, Education Secretary Arne Duncan and civil rights groups have urged lawmakers to strengthen the accountability measures in the bill, but an amendment that aimed to do that didn't get the votes to pass.
It would have required states to identify the lowest-performing five per cent of schools, public high schools where two-thirds or fewer students are graduating on time, and public schools where poor, disabled, minority, or English-language learning children were not meeting state achievement goals. States and schools would then have to design plans to turn around the schools.
"No matter your race or your geography, your disability or your income, you deserve access to a quality education. And if we can't guarantee that, then the question is what good is a federal education law," said Sen. Chris Murphy, D-Conn., who introduced the measure with Democratic Sens. Cory Booker of New Jersey, Elizabeth Warren of Massachusetts, Chris Coons of Delaware and Illinois' Dick Durbin.
Concerned it gave too much power to Washington, Sen. Alexander urged a no vote. The Murphy amendment failed 43-54.
Another amendment, from Sen. Edward Markey, D-Mass., that would have established a climate change education program also was rejected, 44-53.
No Child Left Behind, which had bipartisan support and was signed into law by President George W. 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.