The Every Child Achieves Act, a bipartisan bill to reform the federal education law No Child Left Behind, arrived on the Senate floor for debate on Tuesday, having left committee with unanimous support from Republicans and Democrats.

The bill’s sponsors, Sens. Lamar Alexander, R-Tenn., and Patty Murray, D-Wash., pitched their legislation as a means of significantly reducing burdensome federal mandates in American schooling. The goals of their bill include lowering the “high stakes” associated with standardized tests and allowing states to set their own academic standards. Although states would still be required to administer tests, they would be able to make their own determinations about how to use scores to improve student achievement, how to define which teachers are highly qualified and how to address schools that are failing.

“With so much new federal control of schools over the last several years, this has produced a backlash against Common Core academic standards, teacher evaluation and tests in general,” Alexander said. Common Core is not a federal program. It is math and English standards adopted by the states, but the Obama administration’s encouragement of states to adopt the policy led to some conservative opposition.

He and Murray both said their bill wasn’t perfect, but pledged to fight amendments that would imperil its passage.

“Vouchers are unacceptable to me and would jeopardize our bipartisan work,” Murray said.

Sen. Cory Booker, D-N.J., praised Alexander and Murray, echoing many of their criticisms of No Child Left Behind, but he also stressed that accountability measures are necessary to ensure equality of educational opportunity for all students.

“We must change. However, we cannot allow the pendulum to swing so far that we abdicate our responsibility,” Booker said. “It is not overly prescriptive to ask schools that are failing to graduate a large share of their students to do something differently. It is not overly prescriptive to ask schools — these six percent of our schools that are ‘dropout factories’ in our nation — to make changes, to honor the children, their beauty, their dignity and their potential.”

The Senate is expected to keep debating and amending the Every Child Achieves Act throughout the week. On Monday night, the White House announced that it doesn’t presently support the bill, citing concerns about accountability measures. However, Obama administration officials indicated that they can work with senators on the legislation. In contrast, the White House has pledged to veto a more conservative reform bill currently making its way through the House of Representatives.

But getting the House to find agreement with the Senate is going to be a political challenge, according to Rick Hess, Director of Education Policy Studies for the conservative American Enterprise Institute.

“I think a number of compromises you might get in the Senate, especially from Democratic education reformers, are going to retain more of an outsized federal role,” Hess told InsideSources Tuesday. “If they do, that’s going to make it more difficult to find common ground with the House.”

On the substance, Hess said the Senate bill “gets the big things right” and represents “a vast improvement over the status quo.” He would like to see more “portability” initiatives, wherein money follows children directly, even to private schools. However, he called the Senate legislation “65 percent of a loaf” in terms of the policies he favors.

Follow Graham on Twitter