School kids would still take annual standardized tests, but states would have much more control in how the results are used to scrutinize schools under a bipartisan plan to update the No Child Left Behind education law announced Tuesday by two key senators.

"We have found remarkable consensus about the urgent need to fix this broken law, and also on how to fix it. We look forward to a thorough discussion and debate in the Senate education committee next week," said Sen. Lamar Alexander, R-Tenn., the chairman of the Senate Committee on Health, Education, Labor and Pensions, in a joint press release issued with Sen. Patty Murray, D-Wash., the committee's senior Democrat.

Murray said there's more work to be done, but the agreement is a "strong step in the right direction."

The Senate agreement comes in contrast to a partisan stalemate in the House, where a vote on a GOP-crafted bill to update the Bush-era law was abruptly cancelled in February amid opposition from conservatives concerned that it would continue too strong a federal role in education. House Democrats all along widely opposed the bill, authored by Rep. John Kline, R-Minn., and said it abdicated the federal role in protecting minority, poor and disabled children. The White House threatened to veto it.

The senators announced an April 14 hearing to debate their proposal, which Alexander and Murray have worked on behind closed doors for months. Among the issues they've grappled with is whether to maintain requirements that all students be tested annually in reading and math in grades three to eight and again in high school. Their plan keeps those requirements, but allows states to determine the weight of those tests in how they judge schools.

Initially, Alexander said he was open to debate over federal testing requirements. Murray has supported the requirements as a way to track student progress.

The House bill also keeps the testing requirements.

But, one significant difference is that the senators' proposal does not allow public money to follow low-income children to different public schools, such as charter schools. Some Republicans support allowing public dollars to follow students to both public and private schools.

Despite this consensus, there are still many roadblocks ahead to get the law changed. The House has yet to reschedule a vote, and there's widespread disagreement in Congress over how much of a federal role there should be in identifying and improving failing schools and determining how federal dollars are spent for education.

The No Child Left Behind law, signed in 2002, has been credited with shining a light on the performance of poor, minority, disabled and non-English speaking students, but led to complaints from both Republicans and Democrats that the requirements were unworkable.

The Obama administration in 2012 began allowing waivers around some of the law's more stringent requirements if schools met certain conditions.