WASHINGTON (AP) — The House is trying again to pass a GOP-led rewrite of the Bush-era No Child Left Behind education law, with conservatives aiming to dramatically shift the role of the federal government in education policy away from Washington.

The bill, sponsored by Minnesota Rep. John Kline, would give states and local school districts much more control over accountability for school and teacher performance, similar to a bipartisan bill being debated this week in the Senate. But the House bill includes a provision that has drawn sharp criticism from Democrats — it would allow federal money to follow low-income children to different public schools, an issue known as portability.

Several Democrats went to the House floor Wednesday morning to oppose the bill, with a final vote expected later in the day.

Rep. Eddie Bernice Johnson of Texas urged her colleagues in the House to go back to the drawing board to craft a new bill. “Portability is a ruse, one that takes resources from, rather than gives to, our most underserved and needy children,” said Johnson.

Votes on several amendments are expected later in the afternoon, including one pushed by conservatives to allow states to completely opt out of No Child Left Behind requirements, but still receive federal money in the form of block grants. It’s sponsored by Reps. Mark Walker, R-N.C. and Ron DeSantis, R-Fla.

The House canceled a vote on the Kline bill in February when it became clear it didn’t have enough support from conservatives to pass. This time around, they may have that support.

“We did tell our leadership, if they gave us the chance to vote on some amendments, that we could support the bill even if the amendments fail, and that’s what I intend to do on this bill,” said Rep. Mick Mulvaney, R-S.C. “A lot of just want to be heard and have our chance to try to make the bill better.”

As the House moved forward with debate, the Senate considered a version sponsored by Sen. Lamar Alexander, R-Tenn., and Sen. Patty Murray, D-Wash. Much like the House bill, the measure would whittle away the federal government’s involvement in public schools. It would retain the annual reading and math tests outlined in No Child, but instead it would let states decide how to use the required assessments to measure school and teacher performance.

The bill also would expressly prohibit the federal government from requiring or encouraging any specific set of academic standards — a reference to the Common Core standards, which were drafted by the states with the support of the administration but have become a rallying point for those who want a smaller federal involvement in education.

Alexander has said he expects the Senate bill would lead to fewer tests for America’s children, something many in the education community have complained about, including Education Secretary Arne Duncan.

Murray said she would like stronger measures in the bill that would require states to identify their lowest-performing schools and require those schools to have plans for improvement.

“When we don’t hold our schools and states accountable for educating every child, it is the kids from our low-income backgrounds, kids with disabilities, kids who are learning English and kids of color who too often do fall through the cracks,” Murray said.

No Child Left Behind, which expired in 2007, 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 that the law was rigid and overly ambitious and punitive, and said there was too much testing.

In 2012, the Obama administration began granting states waivers from meeting some of the requirements of the law after it began clear they would not be met. Forty-two states, Puerto Rico and the District of Columbia have been granted waivers.

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Associated Press writer Erica Werner contributed to this report.